Solve Using the Quadratic Formula (x+1)^2+(x-8)^2=45

${(x + 1)}^{2} + {(x - 8)}^{2} = 45$

Move all terms to the left side of the equation and simplify.

Subtract $45$ from both sides of the equation.

${(x + 1)}^{2} + {(x - 8)}^{2} - 45 = 0$

Simplify ${(x + 1)}^{2} + {(x - 8)}^{2} - 45$ .

Simplify each term.

Rewrite ${(x + 1)}^{2}$ as $(x + 1) (x + 1)$ .

$(x + 1) (x + 1) + {(x - 8)}^{2} - 45 = 0$

Expand $(x + 1) (x + 1)$ using the FOIL Method.

Apply the distributive property.

$x (x + 1) + 1 (x + 1) + {(x - 8)}^{2} - 45 = 0$

Apply the distributive property.

$x \cdot x + x \cdot 1 + 1 (x + 1) + {(x - 8)}^{2} - 45 = 0$

Apply the distributive property.

$x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1 + {(x - 8)}^{2} - 45 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 1 + 1 x + 1 \cdot 1 + {(x - 8)}^{2} - 45 = 0$

Multiply $x$ by $1$ .

$x^{2} + x + 1 x + 1 \cdot 1 + {(x - 8)}^{2} - 45 = 0$

Multiply $x$ by $1$ .

$x^{2} + x + x + 1 \cdot 1 + {(x - 8)}^{2} - 45 = 0$

Multiply $1$ by $1$ .

$x^{2} + x + x + 1 + {(x - 8)}^{2} - 45 = 0$

Add $x$ and $x$ .

$x^{2} + 2 x + 1 + {(x - 8)}^{2} - 45 = 0$

Rewrite ${(x - 8)}^{2}$ as $(x - 8) (x - 8)$ .

$x^{2} + 2 x + 1 + (x - 8) (x - 8) - 45 = 0$

Expand $(x - 8) (x - 8)$ using the FOIL Method.

Apply the distributive property.

$x^{2} + 2 x + 1 + x (x - 8) - 8 (x - 8) - 45 = 0$

Apply the distributive property.

$x^{2} + 2 x + 1 + x \cdot x + x \cdot - 8 - 8 (x - 8) - 45 = 0$

Apply the distributive property.

$x^{2} + 2 x + 1 + x \cdot x + x \cdot - 8 - 8 x - 8 \cdot - 8 - 45 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + 2 x + 1 + x^{2} + x \cdot - 8 - 8 x - 8 \cdot - 8 - 45 = 0$

Move $- 8$ to the left of $x$ .

$x^{2} + 2 x + 1 + x^{2} - 8 \cdot x - 8 x - 8 \cdot - 8 - 45 = 0$

Multiply $- 8$ by $- 8$ .

$x^{2} + 2 x + 1 + x^{2} - 8 x - 8 x + 64 - 45 = 0$

Subtract $8 x$ from $- 8 x$ .

$x^{2} + 2 x + 1 + x^{2} - 16 x + 64 - 45 = 0$

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

$2 x^{2} + 2 x + 1 - 16 x + 64 - 45 = 0$

Subtract $16 x$ from $2 x$ .

$2 x^{2} - 14 x + 1 + 64 - 45 = 0$

Add $1$ and $64$ .

$2 x^{2} - 14 x + 65 - 45 = 0$

Subtract $45$ from $65$ .

$2 x^{2} - 14 x + 20 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 2$ , $b = - 14$ , and $c = 20$ into the quadratic formula and solve for $x$ .

$\frac{14 \pm \sqrt{{(- 14)}^{2} - 4 \cdot (2 \cdot 20)}}{2 \cdot 2}$

Simplify.

Simplify the numerator.

Raise $- 14$ to the power of $2$ .

$x = \frac{14 \pm \sqrt{196 - 4 \cdot 2 \cdot 20}}{2 \cdot 2}$

Multiply $- 4$ by $2$ .

$x = \frac{14 \pm \sqrt{196 - 8 \cdot 20}}{2 \cdot 2}$

Multiply $- 8$ by $20$ .

$x = \frac{14 \pm \sqrt{196 - 160}}{2 \cdot 2}$

Subtract $160$ from $196$ .

$x = \frac{14 \pm \sqrt{36}}{2 \cdot 2}$

Rewrite $36$ as $6^{2}$ .

$x = \frac{14 \pm \sqrt{6^{2}}}{2 \cdot 2}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{14 \pm 6}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{14 \pm 6}{4}$

Simplify $\frac{14 \pm 6}{4}$ .

$x = \frac{7 \pm 3}{2}$

The final answer is the combination of both solutions.

$x = 5, 2$

Solve Using the Quadratic Formula (x+1)^2+(x-8)^2=45

Related Questions

Support LCMGCF.com by disabling your adblocker.