Solve Using the Quadratic Formula x^2+x^2=20^2

$x^{2} + x^{2} = 20^{2}$

Step 1

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

Simplify the left side.

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

$2 x^{2} = 20^{2}$

Simplify the right side.

Raise $20$ to the power of $2$ .

$2 x^{2} = 400$

Subtract $400$ from both sides of the equation.

$2 x^{2} - 400 = 0$

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 $a = 2$ , $b = 0$ , and $c = - 400$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (2 \cdot - 400)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 2 \cdot - 400}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 400$ .

Multiply $- 4$ by $2$ .

$x = \frac{0 \pm \sqrt{0 - 8 \cdot - 400}}{2 \cdot 2}$

Multiply $- 8$ by $- 400$ .

$x = \frac{0 \pm \sqrt{0 + 3200}}{2 \cdot 2}$

Add $0$ and $3200$ .

$x = \frac{0 \pm \sqrt{3200}}{2 \cdot 2}$

Rewrite $3200$ as $40^{2} \cdot 2$ .

Factor $1600$ out of $3200$ .

$x = \frac{0 \pm \sqrt{1600 (2)}}{2 \cdot 2}$

Rewrite $1600$ as $40^{2}$ .

$x = \frac{0 \pm \sqrt{40^{2} \cdot 2}}{2 \cdot 2}$

Pull terms out from under the radical.

$x = \frac{0 \pm 40 \sqrt{2}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{0 \pm 40 \sqrt{2}}{4}$

Simplify $\frac{0 \pm 40 \sqrt{2}}{4}$ .

$x = \pm 10 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \pm 10 \sqrt{2}$

Decimal Form:

$x = 14.14213562 \dots, - 14.14213562 \dots$

Solve Using the Quadratic Formula x^2+x^2=20^2

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