Solve 213x^2-15=38

$$213 x ^ { 2 } - 15 = 38$$

Solve for x

$$x=\frac{\sqrt{11289}}{213}\approx 0.49882491$$

$$x=-\frac{\sqrt{11289}}{213}\approx -0.49882491$$

Steps by Finding Square Root

Add 15 to both sides.

$$213x^{2}=38+15$$

Add 38 and 15 to get 53.

$$213x^{2}=53$$

Divide both sides by 213.

$$x^{2}=\frac{53}{213}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{11289}}{213} x=-\frac{\sqrt{11289}}{213}$$

Steps Using the Quadratic Formula

Subtract 38 from both sides.

$$213x^{2}-15-38=0$$

Subtract 38 from -15 to get -53.

$$213x^{2}-53=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 213 for a, 0 for b, and -53 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 213\left(-53\right)}}{2\times 213}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 213\left(-53\right)}}{2\times 213}$$

Multiply -4 times 213.

$$x=\frac{0±\sqrt{-852\left(-53\right)}}{2\times 213}$$

Multiply -852 times -53.

$$x=\frac{0±\sqrt{45156}}{2\times 213}$$

Take the square root of 45156.

$$x=\frac{0±2\sqrt{11289}}{2\times 213}$$

Multiply 2 times 213.

$$x=\frac{0±2\sqrt{11289}}{426}$$

Now solve the equation x=\frac{0±2\sqrt{11289}}{426} when ± is plus.

$$x=\frac{\sqrt{11289}}{213}$$

Now solve the equation x=\frac{0±2\sqrt{11289}}{426} when ± is minus.

$$x=-\frac{\sqrt{11289}}{213}$$

The equation is now solved.

$$x=\frac{\sqrt{11289}}{213} x=-\frac{\sqrt{11289}}{213}$$