Solve x^2=67.24-15.21

$${ x }^{ 2 } =67.24-15.21$$

Solve for x

$$x = \frac{11 \sqrt{43}}{10} \approx 7.213182377$$

$$x = -\frac{11 \sqrt{43}}{10} \approx -7.213182377$$

Steps by Finding Square Root

Subtract 15.21 from 67.24 to get 52.03.

$$x^{2}=52.03$$

Take the square root of both sides of the equation.

$$x=\frac{11\sqrt{43}}{10} x=-\frac{11\sqrt{43}}{10}$$

Steps Using the Quadratic Formula

Subtract 15.21 from 67.24 to get 52.03.

$$x^{2}=52.03$$

Subtract 52.03 from both sides.

$$x^{2}-52.03=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -52.03 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-52.03\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-52.03\right)}}{2}$$

Multiply -4 times -52.03.

$$x=\frac{0±\sqrt{208.12}}{2}$$

Take the square root of 208.12.

$$x=\frac{0±\frac{11\sqrt{43}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{11\sqrt{43}}{5}}{2} when ± is plus.

$$x=\frac{11\sqrt{43}}{10}$$

Now solve the equation x=\frac{0±\frac{11\sqrt{43}}{5}}{2} when ± is minus.

$$x=-\frac{11\sqrt{43}}{10}$$

The equation is now solved.

$$x=\frac{11\sqrt{43}}{10} x=-\frac{11\sqrt{43}}{10}$$