Solve 13x^2=133^2

$$13 x ^ { 2 } = 133 ^ { 2 }$$

Solve for x

$$x = \frac{133 \sqrt{13}}{13} \approx 36.887563049$$

$$x = -\frac{133 \sqrt{13}}{13} \approx -36.887563049$$

Steps by Finding Square Root

Calculate 133 to the power of 2 and get 17689.

$$13x^{2}=17689$$

Divide both sides by 13.

$$x^{2}=\frac{17689}{13}$$

Take the square root of both sides of the equation.

$$x=\frac{133\sqrt{13}}{13} x=-\frac{133\sqrt{13}}{13}$$

Steps Using the Quadratic Formula

Calculate 133 to the power of 2 and get 17689.

$$13x^{2}=17689$$

Subtract 17689 from both sides.

$$13x^{2}-17689=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 13 for a, 0 for b, and -17689 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 13\left(-17689\right)}}{2\times 13}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 13\left(-17689\right)}}{2\times 13}$$

Multiply -4 times 13.

$$x=\frac{0±\sqrt{-52\left(-17689\right)}}{2\times 13}$$

Multiply -52 times -17689.

$$x=\frac{0±\sqrt{919828}}{2\times 13}$$

Take the square root of 919828.

$$x=\frac{0±266\sqrt{13}}{2\times 13}$$

Multiply 2 times 13.

$$x=\frac{0±266\sqrt{13}}{26}$$

Now solve the equation x=\frac{0±266\sqrt{13}}{26} when ± is plus.

$$x=\frac{133\sqrt{13}}{13}$$

Now solve the equation x=\frac{0±266\sqrt{13}}{26} when ± is minus.

$$x=-\frac{133\sqrt{13}}{13}$$

The equation is now solved.

$$x=\frac{133\sqrt{13}}{13} x=-\frac{133\sqrt{13}}{13}$$