Solve 4d^2=64

$$4 d ^ { 2 } = 64$$

Solve for d

$$d=4$$

$$d=-4$$

Steps Using Difference of Squares

Divide both sides by 4.

$$d^{2}=\frac{64}{4}$$

Divide 64 by 4 to get 16.

$$d^{2}=16$$

Subtract 16 from both sides.

$$d^{2}-16=0$$

Consider d^{2}-16. Rewrite d^{2}-16 as d^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(d-4\right)\left(d+4\right)=0$$

To find equation solutions, solve d-4=0 and d+4=0.

$$d=4 d=-4$$

Steps by Finding Square Root

Divide both sides by 4.

$$d^{2}=\frac{64}{4}$$

Divide 64 by 4 to get 16.

$$d^{2}=16$$

Take the square root of both sides of the equation.

$$d=4 d=-4$$

Steps Using the Quadratic Formula

Divide both sides by 4.

$$d^{2}=\frac{64}{4}$$

Divide 64 by 4 to get 16.

$$d^{2}=16$$

Subtract 16 from both sides.

$$d^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$d=\frac{0±\sqrt{0^{2}-4\left(-16\right)}}{2}$$

Square 0.

$$d=\frac{0±\sqrt{-4\left(-16\right)}}{2}$$

Multiply -4 times -16.

$$d=\frac{0±\sqrt{64}}{2}$$

Take the square root of 64.

$$d=\frac{0±8}{2}$$

Now solve the equation d=\frac{0±8}{2} when ± is plus. Divide 8 by 2.

$$d=4$$

Now solve the equation d=\frac{0±8}{2} when ± is minus. Divide -8 by 2.

$$d=-4$$

The equation is now solved.

$$d=4 d=-4$$