Solve (3x)^2=10^2+x^2

$$( 3 x ) ^ { 2 } = 10 ^ { 2 } + x ^ { 2 }$$

Solve for x

$$x = \frac{5 \sqrt{2}}{2} \approx 3.535533906$$

$$x = -\frac{5 \sqrt{2}}{2} \approx -3.535533906$$

Steps by Finding Square Root

Expand \left(3x\right)^{2}.

$$3^{2}x^{2}=10^{2}+x^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}=10^{2}+x^{2}$$

Calculate 10 to the power of 2 and get 100.

$$9x^{2}=100+x^{2}$$

Subtract x^{2} from both sides.

$$9x^{2}-x^{2}=100$$

Combine 9x^{2} and -x^{2} to get 8x^{2}.

$$8x^{2}=100$$

Divide both sides by 8.

$$x^{2}=\frac{100}{8}$$

Reduce the fraction \frac{100}{8} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{25}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{5\sqrt{2}}{2} x=-\frac{5\sqrt{2}}{2}$$

Steps Using the Quadratic Formula

Expand \left(3x\right)^{2}.

$$3^{2}x^{2}=10^{2}+x^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}=10^{2}+x^{2}$$

Calculate 10 to the power of 2 and get 100.

$$9x^{2}=100+x^{2}$$

Subtract 100 from both sides.

$$9x^{2}-100=x^{2}$$

Subtract x^{2} from both sides.

$$9x^{2}-100-x^{2}=0$$

Combine 9x^{2} and -x^{2} to get 8x^{2}.

$$8x^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-100\right)}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-100\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\left(-100\right)}}{2\times 8}$$

Multiply -32 times -100.

$$x=\frac{0±\sqrt{3200}}{2\times 8}$$

Take the square root of 3200.

$$x=\frac{0±40\sqrt{2}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±40\sqrt{2}}{16}$$

Now solve the equation x=\frac{0±40\sqrt{2}}{16} when ± is plus.

$$x=\frac{5\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±40\sqrt{2}}{16} when ± is minus.

$$x=-\frac{5\sqrt{2}}{2}$$

The equation is now solved.

$$x=\frac{5\sqrt{2}}{2} x=-\frac{5\sqrt{2}}{2}$$