Solve -9x^2+4=0

$$- 9 x ^ { 2 } + 4 = 0$$

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

$$x=-\frac{2}{3}\approx -0.666666667$$

Steps by Finding Square Root

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$-9x^{2}=-4$$

Divide both sides by -9.

$$x^{2}=\frac{-4}{-9}$$

Fraction \frac{-4}{-9} can be simplified to \frac{4}{9} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{4}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{2}{3} x=-\frac{2}{3}$$

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.

$$-9x^{2}+4=0$$

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

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

Square 0.

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

Multiply -4 times -9.

$$x=\frac{0±\sqrt{36\times 4}}{2\left(-9\right)}$$

Multiply 36 times 4.

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

Take the square root of 144.

$$x=\frac{0±12}{2\left(-9\right)}$$

Multiply 2 times -9.

$$x=\frac{0±12}{-18}$$

Now solve the equation x=\frac{0±12}{-18} when ± is plus. Reduce the fraction \frac{12}{-18} to lowest terms by extracting and canceling out 6.

$$x=-\frac{2}{3}$$

Now solve the equation x=\frac{0±12}{-18} when ± is minus. Reduce the fraction \frac{-12}{-18} to lowest terms by extracting and canceling out 6.

$$x=\frac{2}{3}$$

The equation is now solved.

$$x=-\frac{2}{3} x=\frac{2}{3}$$