Solve 150-x^2=75

$$150 - x ^ { 2 } = 75$$

Solve for x

$$x=5\sqrt{3}\approx 8.660254038$$

$$x=-5\sqrt{3}\approx -8.660254038$$

Steps by Finding Square Root

Subtract 150 from both sides.

$$-x^{2}=75-150$$

Subtract 150 from 75 to get -75.

$$-x^{2}=-75$$

Divide both sides by -1.

$$x^{2}=\frac{-75}{-1}$$

Fraction \frac{-75}{-1} can be simplified to 75 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=75$$

Take the square root of both sides of the equation.

$$x=5\sqrt{3} x=-5\sqrt{3}$$

Steps Using the Quadratic Formula

Subtract 75 from both sides.

$$150-x^{2}-75=0$$

Subtract 75 from 150 to get 75.

$$75-x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-x^{2}+75=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 75 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 75}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 75}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 75}}{2\left(-1\right)}$$

Multiply 4 times 75.

$$x=\frac{0±\sqrt{300}}{2\left(-1\right)}$$

Take the square root of 300.

$$x=\frac{0±10\sqrt{3}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±10\sqrt{3}}{-2}$$

Now solve the equation x=\frac{0±10\sqrt{3}}{-2} when ± is plus.

$$x=-5\sqrt{3}$$

Now solve the equation x=\frac{0±10\sqrt{3}}{-2} when ± is minus.

$$x=5\sqrt{3}$$

The equation is now solved.

$$x=-5\sqrt{3} x=5\sqrt{3}$$