Find the x and y Intercepts x^2+y^2+8x-8y-17=0

$x^{2} + y^{2} + 8 x - 8 y - 17 = 0$

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$x^{2} + {(0)}^{2} + 8 x - 8 \cdot 0 - 17 = 0$

Solve the equation.

Simplify $x^{2} + {(0)}^{2} + 8 x - 8 \cdot 0 - 17$ .

Simplify each term.

Raising $0$ to any positive power yields $0$ .

$x^{2} + 0 + 8 x - 8 \cdot 0 - 17 = 0$

Multiply $- 8$ by $0$ .

$x^{2} + 0 + 8 x + 0 - 17 = 0$

Combine the opposite terms in $x^{2} + 0 + 8 x + 0 - 17$ .

Add $x^{2}$ and $0$ .

$x^{2} + 8 x + 0 - 17 = 0$

Add $x^{2} + 8 x$ and $0$ .

$x^{2} + 8 x - 17 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 1$ , $b = 8$ , and $c = - 17$ into the quadratic formula and solve for $x$ .

$\frac{- 8 \pm \sqrt{8^{2} - 4 \cdot (1 \cdot - 17)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Raise $8$ to the power of $2$ .

$x = \frac{- 8 \pm \sqrt{64 - 4 \cdot 1 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{- 8 \pm \sqrt{64 - 4 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $- 17$ .

$x = \frac{- 8 \pm \sqrt{64 + 68}}{2 \cdot 1}$

Add $64$ and $68$ .

$x = \frac{- 8 \pm \sqrt{132}}{2 \cdot 1}$

Rewrite $132$ as $2^{2} \cdot 33$ .

Factor $4$ out of $132$ .

$x = \frac{- 8 \pm \sqrt{4 (33)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 8 \pm \sqrt{2^{2} \cdot 33}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 8 \pm 2 \sqrt{33}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 8 \pm 2 \sqrt{33}}{2}$

Simplify $\frac{- 8 \pm 2 \sqrt{33}}{2}$ .

$x = - 4 \pm \sqrt{33}$

Simplify the expression to solve for the $+$ portion of the $\pm$ .

Simplify the numerator.

Raise $8$ to the power of $2$ .

$x = \frac{- 8 \pm \sqrt{64 - 4 \cdot 1 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{- 8 \pm \sqrt{64 - 4 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $- 17$ .

$x = \frac{- 8 \pm \sqrt{64 + 68}}{2 \cdot 1}$

Add $64$ and $68$ .

$x = \frac{- 8 \pm \sqrt{132}}{2 \cdot 1}$

Rewrite $132$ as $2^{2} \cdot 33$ .

Factor $4$ out of $132$ .

$x = \frac{- 8 \pm \sqrt{4 (33)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 8 \pm \sqrt{2^{2} \cdot 33}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 8 \pm 2 \sqrt{33}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 8 \pm 2 \sqrt{33}}{2}$

Simplify $\frac{- 8 \pm 2 \sqrt{33}}{2}$ .

$x = - 4 \pm \sqrt{33}$

Change the $\pm$ to $+$ .

$x = - 4 + \sqrt{33}$

Simplify the expression to solve for the $-$ portion of the $\pm$ .

Simplify the numerator.

Raise $8$ to the power of $2$ .

$x = \frac{- 8 \pm \sqrt{64 - 4 \cdot 1 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{- 8 \pm \sqrt{64 - 4 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $- 17$ .

$x = \frac{- 8 \pm \sqrt{64 + 68}}{2 \cdot 1}$

Add $64$ and $68$ .

$x = \frac{- 8 \pm \sqrt{132}}{2 \cdot 1}$

Rewrite $132$ as $2^{2} \cdot 33$ .

Factor $4$ out of $132$ .

$x = \frac{- 8 \pm \sqrt{4 (33)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 8 \pm \sqrt{2^{2} \cdot 33}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 8 \pm 2 \sqrt{33}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 8 \pm 2 \sqrt{33}}{2}$

Simplify $\frac{- 8 \pm 2 \sqrt{33}}{2}$ .

$x = - 4 \pm \sqrt{33}$

Change the $\pm$ to $-$ .

$x = - 4 - \sqrt{33}$

The final answer is the combination of both solutions.

$x = - 4 + \sqrt{33}, - 4 - \sqrt{33}$

x-intercept(s) in point form.

x-intercept(s): $(- 4 + \sqrt{33}, 0), (- 4 - \sqrt{33}, 0)$

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

${(0)}^{2} + y^{2} + 8 (0) - 8 y - 17 = 0$

Solve the equation.

Simplify ${(0)}^{2} + y^{2} + 8 (0) - 8 y - 17$ .

Simplify each term.

Raising $0$ to any positive power yields $0$ .

$0 + y^{2} + 8 (0) - 8 y - 17 = 0$

Multiply $8$ by $0$ .

$0 + y^{2} + 0 - 8 y - 17 = 0$

Combine the opposite terms in $0 + y^{2} + 0 - 8 y - 17$ .

Add $0$ and $y^{2}$ .

$y^{2} + 0 - 8 y - 17 = 0$

Add $y^{2}$ and $0$ .

$y^{2} - 8 y - 17 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 1$ , $b = - 8$ , and $c = - 17$ into the quadratic formula and solve for $y$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (1 \cdot - 17)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$y = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$y = \frac{8 \pm \sqrt{64 - 4 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $- 17$ .

$y = \frac{8 \pm \sqrt{64 + 68}}{2 \cdot 1}$

Add $64$ and $68$ .

$y = \frac{8 \pm \sqrt{132}}{2 \cdot 1}$

Rewrite $132$ as $2^{2} \cdot 33$ .

Factor $4$ out of $132$ .

$y = \frac{8 \pm \sqrt{4 (33)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$y = \frac{8 \pm \sqrt{2^{2} \cdot 33}}{2 \cdot 1}$

Pull terms out from under the radical.

$y = \frac{8 \pm 2 \sqrt{33}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{8 \pm 2 \sqrt{33}}{2}$

Simplify $\frac{8 \pm 2 \sqrt{33}}{2}$ .

$y = 4 \pm \sqrt{33}$

Simplify the expression to solve for the $+$ portion of the $\pm$ .

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$y = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$y = \frac{8 \pm \sqrt{64 - 4 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $- 17$ .

$y = \frac{8 \pm \sqrt{64 + 68}}{2 \cdot 1}$

Add $64$ and $68$ .

$y = \frac{8 \pm \sqrt{132}}{2 \cdot 1}$

Rewrite $132$ as $2^{2} \cdot 33$ .

Factor $4$ out of $132$ .

$y = \frac{8 \pm \sqrt{4 (33)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$y = \frac{8 \pm \sqrt{2^{2} \cdot 33}}{2 \cdot 1}$

Pull terms out from under the radical.

$y = \frac{8 \pm 2 \sqrt{33}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{8 \pm 2 \sqrt{33}}{2}$

Simplify $\frac{8 \pm 2 \sqrt{33}}{2}$ .

$y = 4 \pm \sqrt{33}$

Change the $\pm$ to $+$ .

$y = 4 + \sqrt{33}$

Simplify the expression to solve for the $-$ portion of the $\pm$ .

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$y = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$y = \frac{8 \pm \sqrt{64 - 4 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $- 17$ .

$y = \frac{8 \pm \sqrt{64 + 68}}{2 \cdot 1}$

Add $64$ and $68$ .

$y = \frac{8 \pm \sqrt{132}}{2 \cdot 1}$

Rewrite $132$ as $2^{2} \cdot 33$ .

Factor $4$ out of $132$ .

$y = \frac{8 \pm \sqrt{4 (33)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$y = \frac{8 \pm \sqrt{2^{2} \cdot 33}}{2 \cdot 1}$

Pull terms out from under the radical.

$y = \frac{8 \pm 2 \sqrt{33}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{8 \pm 2 \sqrt{33}}{2}$

Simplify $\frac{8 \pm 2 \sqrt{33}}{2}$ .

$y = 4 \pm \sqrt{33}$

Change the $\pm$ to $-$ .

$y = 4 - \sqrt{33}$

The final answer is the combination of both solutions.

$y = 4 + \sqrt{33}, 4 - \sqrt{33}$

y-intercept(s) in point form.

y-intercept(s): $(0, 4 + \sqrt{33}), (0, 4 - \sqrt{33})$

List the intersections.

x-intercept(s): $(- 4 + \sqrt{33}, 0), (- 4 - \sqrt{33}, 0)$

y-intercept(s): $(0, 4 + \sqrt{33}), (0, 4 - \sqrt{33})$

Find the x and y Intercepts x^2+y^2+8x-8y-17=0

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