Solve (2x)^2-x^2=30^2

$$( 2 x ) ^ { 2 } - x ^ { 2 } = 30 ^ { 2 }$$

Solve for x

$$x=10\sqrt{3}\approx 17.320508076$$

$$x=-10\sqrt{3}\approx -17.320508076$$

Steps by Finding Square Root

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

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

Calculate 2 to the power of 2 and get 4.

$$4x^{2}-x^{2}=30^{2}$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}=30^{2}$$

Calculate 30 to the power of 2 and get 900.

$$3x^{2}=900$$

Divide both sides by 3.

$$x^{2}=\frac{900}{3}$$

Divide 900 by 3 to get 300.

$$x^{2}=300$$

Take the square root of both sides of the equation.

$$x=10\sqrt{3} x=-10\sqrt{3}$$

Steps Using the Quadratic Formula

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

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

Calculate 2 to the power of 2 and get 4.

$$4x^{2}-x^{2}=30^{2}$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}=30^{2}$$

Calculate 30 to the power of 2 and get 900.

$$3x^{2}=900$$

Subtract 900 from both sides.

$$3x^{2}-900=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -900 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-900\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-900\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-900\right)}}{2\times 3}$$

Multiply -12 times -900.

$$x=\frac{0±\sqrt{10800}}{2\times 3}$$

Take the square root of 10800.

$$x=\frac{0±60\sqrt{3}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±60\sqrt{3}}{6}$$

Now solve the equation x=\frac{0±60\sqrt{3}}{6} when ± is plus.

$$x=10\sqrt{3}$$

Now solve the equation x=\frac{0±60\sqrt{3}}{6} when ± is minus.

$$x=-10\sqrt{3}$$

The equation is now solved.

$$x=10\sqrt{3} x=-10\sqrt{3}$$