Solve (x)^2+(6x)^2=(30)^2

$$( x ) ^ { 2 } + ( 6 x ) ^ { 2 } = ( 30 ) ^ { 2 }$$

Solve for x

$$x = \frac{30 \sqrt{37}}{37} \approx 4.931969619$$

$$x = -\frac{30 \sqrt{37}}{37} \approx -4.931969619$$

Steps by Finding Square Root

Expand \left(6x\right)^{2}.

$$x^{2}+6^{2}x^{2}=30^{2}$$

Calculate 6 to the power of 2 and get 36.

$$x^{2}+36x^{2}=30^{2}$$

Combine x^{2} and 36x^{2} to get 37x^{2}.

$$37x^{2}=30^{2}$$

Calculate 30 to the power of 2 and get 900.

$$37x^{2}=900$$

Divide both sides by 37.

$$x^{2}=\frac{900}{37}$$

Take the square root of both sides of the equation.

$$x=\frac{30\sqrt{37}}{37} x=-\frac{30\sqrt{37}}{37}$$

Steps Using the Quadratic Formula

Expand \left(6x\right)^{2}.

$$x^{2}+6^{2}x^{2}=30^{2}$$

Calculate 6 to the power of 2 and get 36.

$$x^{2}+36x^{2}=30^{2}$$

Combine x^{2} and 36x^{2} to get 37x^{2}.

$$37x^{2}=30^{2}$$

Calculate 30 to the power of 2 and get 900.

$$37x^{2}=900$$

Subtract 900 from both sides.

$$37x^{2}-900=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 37 for a, 0 for b, and -900 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 37\left(-900\right)}}{2\times 37}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 37\left(-900\right)}}{2\times 37}$$

Multiply -4 times 37.

$$x=\frac{0±\sqrt{-148\left(-900\right)}}{2\times 37}$$

Multiply -148 times -900.

$$x=\frac{0±\sqrt{133200}}{2\times 37}$$

Take the square root of 133200.

$$x=\frac{0±60\sqrt{37}}{2\times 37}$$

Multiply 2 times 37.

$$x=\frac{0±60\sqrt{37}}{74}$$

Now solve the equation x=\frac{0±60\sqrt{37}}{74} when ± is plus.

$$x=\frac{30\sqrt{37}}{37}$$

Now solve the equation x=\frac{0±60\sqrt{37}}{74} when ± is minus.

$$x=-\frac{30\sqrt{37}}{37}$$

The equation is now solved.

$$x=\frac{30\sqrt{37}}{37} x=-\frac{30\sqrt{37}}{37}$$