Solve -18=-98d^2

$$- 18 = - 98 d ^ { 2 }$$

Solve for d

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

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

Steps Using Difference of Squares

Divide both sides by -98.

$$\frac{-18}{-98}=d^{2}$$

Reduce the fraction \frac{-18}{-98} to lowest terms by extracting and canceling out -2.

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

Swap sides so that all variable terms are on the left hand side.

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

Subtract \frac{9}{49} from both sides.

$$d^{2}-\frac{9}{49}=0$$

Multiply both sides by 49.

$$49d^{2}-9=0$$

Consider 49d^{2}-9. Rewrite 49d^{2}-9 as \left(7d\right)^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(7d-3\right)\left(7d+3\right)=0$$

To find equation solutions, solve 7d-3=0 and 7d+3=0.

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

Steps by Finding Square Root

Divide both sides by -98.

$$\frac{-18}{-98}=d^{2}$$

Reduce the fraction \frac{-18}{-98} to lowest terms by extracting and canceling out -2.

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

Swap sides so that all variable terms are on the left hand side.

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

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Divide both sides by -98.

$$\frac{-18}{-98}=d^{2}$$

Reduce the fraction \frac{-18}{-98} to lowest terms by extracting and canceling out -2.

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

Swap sides so that all variable terms are on the left hand side.

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

Subtract \frac{9}{49} from both sides.

$$d^{2}-\frac{9}{49}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{9}{49} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -\frac{9}{49}.

$$d=\frac{0±\sqrt{\frac{36}{49}}}{2}$$

Take the square root of \frac{36}{49}.

$$d=\frac{0±\frac{6}{7}}{2}$$

Now solve the equation d=\frac{0±\frac{6}{7}}{2} when ± is plus.

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

Now solve the equation d=\frac{0±\frac{6}{7}}{2} when ± is minus.

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

The equation is now solved.

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