Solve 15^2=x^2+x^2

$$15 ^ { 2 } = x ^ { 2 } + x ^ { 2 }$$

Solve for x

$$x = \frac{15 \sqrt{2}}{2} \approx 10.606601718$$

$$x = -\frac{15 \sqrt{2}}{2} \approx -10.606601718$$

Steps by Finding Square Root

Calculate 15 to the power of 2 and get 225.

$$225=x^{2}+x^{2}$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$225=2x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$2x^{2}=225$$

Divide both sides by 2.

$$x^{2}=\frac{225}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{15\sqrt{2}}{2} x=-\frac{15\sqrt{2}}{2}$$

Steps Using the Quadratic Formula

Calculate 15 to the power of 2 and get 225.

$$225=x^{2}+x^{2}$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$225=2x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$2x^{2}=225$$

Subtract 225 from both sides.

$$2x^{2}-225=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -225 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-225\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-225\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-225\right)}}{2\times 2}$$

Multiply -8 times -225.

$$x=\frac{0±\sqrt{1800}}{2\times 2}$$

Take the square root of 1800.

$$x=\frac{0±30\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±30\sqrt{2}}{4}$$

Now solve the equation x=\frac{0±30\sqrt{2}}{4} when ± is plus.

$$x=\frac{15\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±30\sqrt{2}}{4} when ± is minus.

$$x=-\frac{15\sqrt{2}}{2}$$

The equation is now solved.

$$x=\frac{15\sqrt{2}}{2} x=-\frac{15\sqrt{2}}{2}$$