Solve -9h^2+1=0

$$- 9 h ^ { 2 } + 1 = 0$$

Solve for h

$$h=\frac{1}{3}\approx 0.333333333$$

$$h=-\frac{1}{3}\approx -0.333333333$$

Steps by Finding Square Root

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-9h^{2}=-1$$

Divide both sides by -9.

$$h^{2}=\frac{-1}{-9}$$

Fraction \frac{-1}{-9} can be simplified to \frac{1}{9} by removing the negative sign from both the numerator and the denominator.

$$h^{2}=\frac{1}{9}$$

Take the square root of both sides of the equation.

$$h=\frac{1}{3} h=-\frac{1}{3}$$

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.

$$-9h^{2}+1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -9 for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -9.

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

Take the square root of 36.

$$h=\frac{0±6}{2\left(-9\right)}$$

Multiply 2 times -9.

$$h=\frac{0±6}{-18}$$

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

$$h=-\frac{1}{3}$$

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

$$h=\frac{1}{3}$$

The equation is now solved.

$$h=-\frac{1}{3} h=\frac{1}{3}$$