Solve Using the Quadratic Formula 8^2+10^2=x^2

$8^{2} + 10^{2} = x^{2}$

Step 1

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

Simplify the left side.

Simplify $8^{2} + 10^{2}$ .

Simplify each term.

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

$64 + 10^{2} = x^{2}$

Raise $10$ to the power of $2$ .

$64 + 100 = x^{2}$

Add $64$ and $100$ .

$164 = x^{2}$

Subtract $x^{2}$ from both sides of the equation.

$164 - x^{2} = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = - 1$ , $b = 0$ , and $c = 164$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (- 1 \cdot 164)}}{2 \cdot - 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 1 \cdot 164}}{2 \cdot - 1}$

Multiply $- 4 \cdot - 1 \cdot 164$ .

Multiply $- 4$ by $- 1$ .

$x = \frac{0 \pm \sqrt{0 + 4 \cdot 164}}{2 \cdot - 1}$

Multiply $4$ by $164$ .

$x = \frac{0 \pm \sqrt{0 + 656}}{2 \cdot - 1}$

Add $0$ and $656$ .

$x = \frac{0 \pm \sqrt{656}}{2 \cdot - 1}$

Rewrite $656$ as $4^{2} \cdot 41$ .

Factor $16$ out of $656$ .

$x = \frac{0 \pm \sqrt{16 (41)}}{2 \cdot - 1}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{0 \pm \sqrt{4^{2} \cdot 41}}{2 \cdot - 1}$

Pull terms out from under the radical.

$x = \frac{0 \pm 4 \sqrt{41}}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$x = \frac{0 \pm 4 \sqrt{41}}{- 2}$

Simplify $\frac{0 \pm 4 \sqrt{41}}{- 2}$ .

$x = \pm 2 \sqrt{41}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \pm 2 \sqrt{41}$

Decimal Form:

$x = 12.80624847 \dots, - 12.80624847 \dots$

Solve Using the Quadratic Formula 8^2+10^2=x^2

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