Solve 3d^2-147=0

$$3 d ^ { 2 } - 147 = 0$$

Solve for d

$$d=7$$

$$d=-7$$

Steps Using Difference of Squares

Divide both sides by 3.

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

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

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

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

$$d=7 d=-7$$

Steps by Finding Square Root

Add 147 to both sides. Anything plus zero gives itself.

$$3d^{2}=147$$

Divide both sides by 3.

$$d^{2}=\frac{147}{3}$$

Divide 147 by 3 to get 49.

$$d^{2}=49$$

Take the square root of both sides of the equation.

$$d=7 d=-7$$

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.

$$3d^{2}-147=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -147 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$d=\frac{0±\sqrt{0^{2}-4\times 3\left(-147\right)}}{2\times 3}$$

Square 0.

$$d=\frac{0±\sqrt{-4\times 3\left(-147\right)}}{2\times 3}$$

Multiply -4 times 3.

$$d=\frac{0±\sqrt{-12\left(-147\right)}}{2\times 3}$$

Multiply -12 times -147.

$$d=\frac{0±\sqrt{1764}}{2\times 3}$$

Take the square root of 1764.

$$d=\frac{0±42}{2\times 3}$$

Multiply 2 times 3.

$$d=\frac{0±42}{6}$$

Now solve the equation d=\frac{0±42}{6} when ± is plus. Divide 42 by 6.

$$d=7$$

Now solve the equation d=\frac{0±42}{6} when ± is minus. Divide -42 by 6.

$$d=-7$$

The equation is now solved.

$$d=7 d=-7$$