Solve x^2=52-48*0.3

$${ x }^{ 2 } =52-48 \times 0.3$$

Solve for x

$$x = \frac{2 \sqrt{235}}{5} \approx 6.131883887$$

$$x = -\frac{2 \sqrt{235}}{5} \approx -6.131883887$$

Steps by Finding Square Root

Multiply 48 and 0.3 to get 14.4.

$$x^{2}=52-14.4$$

Subtract 14.4 from 52 to get 37.6.

$$x^{2}=37.6$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{235}}{5} x=-\frac{2\sqrt{235}}{5}$$

Steps Using the Quadratic Formula

Multiply 48 and 0.3 to get 14.4.

$$x^{2}=52-14.4$$

Subtract 14.4 from 52 to get 37.6.

$$x^{2}=37.6$$

Subtract 37.6 from both sides.

$$x^{2}-37.6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -37.6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-37.6\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-37.6\right)}}{2}$$

Multiply -4 times -37.6.

$$x=\frac{0±\sqrt{150.4}}{2}$$

Take the square root of 150.4.

$$x=\frac{0±\frac{4\sqrt{235}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{235}}{5}}{2} when ± is plus.

$$x=\frac{2\sqrt{235}}{5}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{235}}{5}}{2} when ± is minus.

$$x=-\frac{2\sqrt{235}}{5}$$

The equation is now solved.

$$x=\frac{2\sqrt{235}}{5} x=-\frac{2\sqrt{235}}{5}$$