Solve 7s^2-7=0

$$7 s ^ { 2 } - 7 = 0$$

Solve for s

$$s=1$$

$$s=-1$$

Steps Using Difference of Squares

Divide both sides by 7.

$$s^{2}-1=0$$

Consider s^{2}-1. Rewrite s^{2}-1 as s^{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).

$$\left(s-1\right)\left(s+1\right)=0$$

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

$$s=1 s=-1$$

Steps by Finding Square Root

Add 7 to both sides. Anything plus zero gives itself.

$$7s^{2}=7$$

Divide both sides by 7.

$$s^{2}=\frac{7}{7}$$

Divide 7 by 7 to get 1.

$$s^{2}=1$$

Take the square root of both sides of the equation.

$$s=1 s=-1$$

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.

$$7s^{2}-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s=\frac{0±\sqrt{0^{2}-4\times 7\left(-7\right)}}{2\times 7}$$

Square 0.

$$s=\frac{0±\sqrt{-4\times 7\left(-7\right)}}{2\times 7}$$

Multiply -4 times 7.

$$s=\frac{0±\sqrt{-28\left(-7\right)}}{2\times 7}$$

Multiply -28 times -7.

$$s=\frac{0±\sqrt{196}}{2\times 7}$$

Take the square root of 196.

$$s=\frac{0±14}{2\times 7}$$

Multiply 2 times 7.

$$s=\frac{0±14}{14}$$

Now solve the equation s=\frac{0±14}{14} when ± is plus. Divide 14 by 14.

$$s=1$$

Now solve the equation s=\frac{0±14}{14} when ± is minus. Divide -14 by 14.

$$s=-1$$

The equation is now solved.

$$s=1 s=-1$$