Solve 400d^2-1=0

$$400 d ^ { 2 } - 1 = 0$$

Solve for d

$$d=\frac{1}{20}=0.05$$

$$d=-\frac{1}{20}=-0.05$$

Steps Using Difference of Squares

Consider 400d^{2}-1. Rewrite 400d^{2}-1 as \left(20d\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(20d-1\right)\left(20d+1\right)=0$$

To find equation solutions, solve 20d-1=0 and 20d+1=0.

$$d=\frac{1}{20} d=-\frac{1}{20}$$

Steps by Finding Square Root

Add 1 to both sides. Anything plus zero gives itself.

$$400d^{2}=1$$

Divide both sides by 400.

$$d^{2}=\frac{1}{400}$$

Take the square root of both sides of the equation.

$$d=\frac{1}{20} d=-\frac{1}{20}$$

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.

$$400d^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 400 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$d=\frac{0±\sqrt{0^{2}-4\times 400\left(-1\right)}}{2\times 400}$$

Square 0.

$$d=\frac{0±\sqrt{-4\times 400\left(-1\right)}}{2\times 400}$$

Multiply -4 times 400.

$$d=\frac{0±\sqrt{-1600\left(-1\right)}}{2\times 400}$$

Multiply -1600 times -1.

$$d=\frac{0±\sqrt{1600}}{2\times 400}$$

Take the square root of 1600.

$$d=\frac{0±40}{2\times 400}$$

Multiply 2 times 400.

$$d=\frac{0±40}{800}$$

Now solve the equation d=\frac{0±40}{800} when ± is plus. Reduce the fraction \frac{40}{800} to lowest terms by extracting and canceling out 40.

$$d=\frac{1}{20}$$

Now solve the equation d=\frac{0±40}{800} when ± is minus. Reduce the fraction \frac{-40}{800} to lowest terms by extracting and canceling out 40.

$$d=-\frac{1}{20}$$

The equation is now solved.

$$d=\frac{1}{20} d=-\frac{1}{20}$$