Solve -9j^2+8=0

$$- 9 j ^ { 2 } + 8 = 0$$

Solve for j

$$j=\frac{2\sqrt{2}}{3}\approx 0.942809042$$

$$j=-\frac{2\sqrt{2}}{3}\approx -0.942809042$$

Steps by Finding Square Root

Subtract 8 from both sides. Anything subtracted from zero gives its negation.

$$-9j^{2}=-8$$

Divide both sides by -9.

$$j^{2}=\frac{-8}{-9}$$

Fraction \frac{-8}{-9} can be simplified to \frac{8}{9} by removing the negative sign from both the numerator and the denominator.

$$j^{2}=\frac{8}{9}$$

Take the square root of both sides of the equation.

$$j=\frac{2\sqrt{2}}{3} j=-\frac{2\sqrt{2}}{3}$$

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.

$$-9j^{2}+8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -9 for a, 0 for b, and 8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$j=\frac{0±\sqrt{0^{2}-4\left(-9\right)\times 8}}{2\left(-9\right)}$$

Square 0.

$$j=\frac{0±\sqrt{-4\left(-9\right)\times 8}}{2\left(-9\right)}$$

Multiply -4 times -9.

$$j=\frac{0±\sqrt{36\times 8}}{2\left(-9\right)}$$

Multiply 36 times 8.

$$j=\frac{0±\sqrt{288}}{2\left(-9\right)}$$

Take the square root of 288.

$$j=\frac{0±12\sqrt{2}}{2\left(-9\right)}$$

Multiply 2 times -9.

$$j=\frac{0±12\sqrt{2}}{-18}$$

Now solve the equation j=\frac{0±12\sqrt{2}}{-18} when ± is plus.

$$j=-\frac{2\sqrt{2}}{3}$$

Now solve the equation j=\frac{0±12\sqrt{2}}{-18} when ± is minus.

$$j=\frac{2\sqrt{2}}{3}$$

The equation is now solved.

$$j=-\frac{2\sqrt{2}}{3} j=\frac{2\sqrt{2}}{3}$$