Solve left(3xright)^2+20-4x^2=13^2

$${ \left(3x \right) }^{ 2 } +20-4 { x }^{ 2 } = { 13 }^{ 2 }$$

Solve for x

$$x = \frac{\sqrt{745}}{5} \approx 5.458937626$$

$$x = -\frac{\sqrt{745}}{5} \approx -5.458937626$$

Steps by Finding Square Root

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

$$3^{2}x^{2}+20-4x^{2}=13^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}+20-4x^{2}=13^{2}$$

Combine 9x^{2} and -4x^{2} to get 5x^{2}.

$$5x^{2}+20=13^{2}$$

Calculate 13 to the power of 2 and get 169.

$$5x^{2}+20=169$$

Subtract 20 from both sides.

$$5x^{2}=169-20$$

Subtract 20 from 169 to get 149.

$$5x^{2}=149$$

Divide both sides by 5.

$$x^{2}=\frac{149}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{745}}{5} x=-\frac{\sqrt{745}}{5}$$

Steps Using the Quadratic Formula

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

$$3^{2}x^{2}+20-4x^{2}=13^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}+20-4x^{2}=13^{2}$$

Combine 9x^{2} and -4x^{2} to get 5x^{2}.

$$5x^{2}+20=13^{2}$$

Calculate 13 to the power of 2 and get 169.

$$5x^{2}+20=169$$

Subtract 169 from both sides.

$$5x^{2}+20-169=0$$

Subtract 169 from 20 to get -149.

$$5x^{2}-149=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -149 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-149\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-149\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-149\right)}}{2\times 5}$$

Multiply -20 times -149.

$$x=\frac{0±\sqrt{2980}}{2\times 5}$$

Take the square root of 2980.

$$x=\frac{0±2\sqrt{745}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±2\sqrt{745}}{10}$$

Now solve the equation x=\frac{0±2\sqrt{745}}{10} when ± is plus.

$$x=\frac{\sqrt{745}}{5}$$

Now solve the equation x=\frac{0±2\sqrt{745}}{10} when ± is minus.

$$x=-\frac{\sqrt{745}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{745}}{5} x=-\frac{\sqrt{745}}{5}$$