Solve -49w^2+9=0

$$- 49 w ^ { 2 } + 9 = 0$$

Solve for w

$$w=\frac{3}{7}\approx 0.428571429$$

$$w=-\frac{3}{7}\approx -0.428571429$$

Steps by Finding Square Root

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$-49w^{2}=-9$$

Divide both sides by -49.

$$w^{2}=\frac{-9}{-49}$$

Fraction \frac{-9}{-49} can be simplified to \frac{9}{49} by removing the negative sign from both the numerator and the denominator.

$$w^{2}=\frac{9}{49}$$

Take the square root of both sides of the equation.

$$w=\frac{3}{7} w=-\frac{3}{7}$$

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.

$$-49w^{2}+9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -49 for a, 0 for b, and 9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{0±\sqrt{0^{2}-4\left(-49\right)\times 9}}{2\left(-49\right)}$$

Square 0.

$$w=\frac{0±\sqrt{-4\left(-49\right)\times 9}}{2\left(-49\right)}$$

Multiply -4 times -49.

$$w=\frac{0±\sqrt{196\times 9}}{2\left(-49\right)}$$

Multiply 196 times 9.

$$w=\frac{0±\sqrt{1764}}{2\left(-49\right)}$$

Take the square root of 1764.

$$w=\frac{0±42}{2\left(-49\right)}$$

Multiply 2 times -49.

$$w=\frac{0±42}{-98}$$

Now solve the equation w=\frac{0±42}{-98} when ± is plus. Reduce the fraction \frac{42}{-98} to lowest terms by extracting and canceling out 14.

$$w=-\frac{3}{7}$$

Now solve the equation w=\frac{0±42}{-98} when ± is minus. Reduce the fraction \frac{-42}{-98} to lowest terms by extracting and canceling out 14.

$$w=\frac{3}{7}$$

The equation is now solved.

$$w=-\frac{3}{7} w=\frac{3}{7}$$