Solve -9x^2+144=0

$$-9 { x }^{ 2 } +144=0$$

Solve for x

$$x=4$$

$$x=-4$$

Steps by Finding Square Root

Subtract 144 from both sides. Anything subtracted from zero gives its negation.

$$-9x^{2}=-144$$

Divide both sides by -9.

$$x^{2}=\frac{-144}{-9}$$

Divide -144 by -9 to get 16.

$$x^{2}=16$$

Take the square root of both sides of the equation.

$$x=4 x=-4$$

Steps Using the Quadratic Formula

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.

$$-9x^{2}+144=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -9 for a, 0 for b, and 144 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-9\right)\times 144}}{2\left(-9\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-9\right)\times 144}}{2\left(-9\right)}$$

Multiply -4 times -9.

$$x=\frac{0±\sqrt{36\times 144}}{2\left(-9\right)}$$

Multiply 36 times 144.

$$x=\frac{0±\sqrt{5184}}{2\left(-9\right)}$$

Take the square root of 5184.

$$x=\frac{0±72}{2\left(-9\right)}$$

Multiply 2 times -9.

$$x=\frac{0±72}{-18}$$

Now solve the equation x=\frac{0±72}{-18} when ± is plus. Divide 72 by -18.

$$x=-4$$

Now solve the equation x=\frac{0±72}{-18} when ± is minus. Divide -72 by -18.

$$x=4$$

The equation is now solved.

$$x=-4 x=4$$