Write in Standard Form x=y^2-8y-11

$x = y^{2} - 8 y - 11$

Solve for $y$ .

Rewrite the equation as $y^{2} - 8 y - 11 = x$ .

$y^{2} - 8 y - 11 = x$

Subtract $x$ from both sides of the equation.

$y^{2} - 8 y - 11 - x = 0$

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 $c = - 11 - x$ into the quadratic formula and solve for $y$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (1 \cdot (- 11 - x))}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

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

$y = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot (- 11 - x)}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$y = \frac{8 \pm \sqrt{64 - 4 \cdot (- 11 - x)}}{2 \cdot 1}$

Apply the distributive property.

$y = \frac{8 \pm \sqrt{64 - 4 \cdot - 11 - 4 (- x)}}{2 \cdot 1}$

Multiply $- 4$ by $- 11$ .

$y = \frac{8 \pm \sqrt{64 + 44 - 4 (- x)}}{2 \cdot 1}$

Multiply $- 1$ by $- 4$ .

$y = \frac{8 \pm \sqrt{64 + 44 + 4 x}}{2 \cdot 1}$

Add $64$ and $44$ .

$y = \frac{8 \pm \sqrt{108 + 4 x}}{2 \cdot 1}$

Factor $4$ out of $108 + 4 x$ .

Factor $4$ out of $108$ .

$y = \frac{8 \pm \sqrt{4 \cdot 27 + 4 x}}{2 \cdot 1}$

Factor $4$ out of $4 \cdot 27 + 4 x$ .

$y = \frac{8 \pm \sqrt{4 (27 + x)}}{2 \cdot 1}$

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

$y = \frac{8 \pm \sqrt{2^{2} (27 + x)}}{2 \cdot 1}$

Pull terms out from under the radical.

$y = \frac{8 \pm 2 \sqrt{27 + x}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{8 \pm 2 \sqrt{27 + x}}{2}$

Simplify $\frac{8 \pm 2 \sqrt{27 + x}}{2}$ .

$y = 4 \pm \sqrt{27 + x}$

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

Simplify the numerator.

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

$y = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot (- 11 - x)}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$y = \frac{8 \pm \sqrt{64 - 4 \cdot (- 11 - x)}}{2 \cdot 1}$

Apply the distributive property.

$y = \frac{8 \pm \sqrt{64 - 4 \cdot - 11 - 4 (- x)}}{2 \cdot 1}$

Multiply $- 4$ by $- 11$ .

$y = \frac{8 \pm \sqrt{64 + 44 - 4 (- x)}}{2 \cdot 1}$

Multiply $- 1$ by $- 4$ .

$y = \frac{8 \pm \sqrt{64 + 44 + 4 x}}{2 \cdot 1}$

Add $64$ and $44$ .

$y = \frac{8 \pm \sqrt{108 + 4 x}}{2 \cdot 1}$

Factor $4$ out of $108 + 4 x$ .

Factor $4$ out of $108$ .

$y = \frac{8 \pm \sqrt{4 \cdot 27 + 4 x}}{2 \cdot 1}$

Factor $4$ out of $4 \cdot 27 + 4 x$ .

$y = \frac{8 \pm \sqrt{4 (27 + x)}}{2 \cdot 1}$

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

$y = \frac{8 \pm \sqrt{2^{2} (27 + x)}}{2 \cdot 1}$

Pull terms out from under the radical.

$y = \frac{8 \pm 2 \sqrt{27 + x}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{8 \pm 2 \sqrt{27 + x}}{2}$

Simplify $\frac{8 \pm 2 \sqrt{27 + x}}{2}$ .

$y = 4 \pm \sqrt{27 + x}$

Change the $\pm$ to $+$ .

$y = 4 + \sqrt{27 + x}$

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

Simplify the numerator.

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

$y = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot (- 11 - x)}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$y = \frac{8 \pm \sqrt{64 - 4 \cdot (- 11 - x)}}{2 \cdot 1}$

Apply the distributive property.

$y = \frac{8 \pm \sqrt{64 - 4 \cdot - 11 - 4 (- x)}}{2 \cdot 1}$

Multiply $- 4$ by $- 11$ .

$y = \frac{8 \pm \sqrt{64 + 44 - 4 (- x)}}{2 \cdot 1}$

Multiply $- 1$ by $- 4$ .

$y = \frac{8 \pm \sqrt{64 + 44 + 4 x}}{2 \cdot 1}$

Add $64$ and $44$ .

$y = \frac{8 \pm \sqrt{108 + 4 x}}{2 \cdot 1}$

Factor $4$ out of $108 + 4 x$ .

Factor $4$ out of $108$ .

$y = \frac{8 \pm \sqrt{4 \cdot 27 + 4 x}}{2 \cdot 1}$

Factor $4$ out of $4 \cdot 27 + 4 x$ .

$y = \frac{8 \pm \sqrt{4 (27 + x)}}{2 \cdot 1}$

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

$y = \frac{8 \pm \sqrt{2^{2} (27 + x)}}{2 \cdot 1}$

Pull terms out from under the radical.

$y = \frac{8 \pm 2 \sqrt{27 + x}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{8 \pm 2 \sqrt{27 + x}}{2}$

Simplify $\frac{8 \pm 2 \sqrt{27 + x}}{2}$ .

$y = 4 \pm \sqrt{27 + x}$

Change the $\pm$ to $-$ .

$y = 4 - \sqrt{27 + x}$

The final answer is the combination of both solutions.

$y = 4 + \sqrt{27 + x}$

$y = 4 - \sqrt{27 + x}$

$y = 4 + \sqrt{27 + x}$

$y = 4 - \sqrt{27 + x}$

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$y = a x^{2} + b x + c$

The standard form is $4 + \sqrt{27 + x}, 4 - \sqrt{27 + x}$ .

$y = 4 + \sqrt{27 + x}$

$y = 4 - \sqrt{27 + x}$

Write in Standard Form x=y^2-8y-11

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