Solve 6s^2-5=19

$$6 s ^ { 2 } - 5 = 19$$

Solve for s

$$s=2$$

$$s=-2$$

Steps Using Difference of Squares

Subtract 19 from both sides.

$$6s^{2}-5-19=0$$

Subtract 19 from -5 to get -24.

$$6s^{2}-24=0$$

Divide both sides by 6.

$$s^{2}-4=0$$

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

$$\left(s-2\right)\left(s+2\right)=0$$

To find equation solutions, solve s-2=0 and s+2=0.

$$s=2 s=-2$$

Steps by Finding Square Root

Add 5 to both sides.

$$6s^{2}=19+5$$

Add 19 and 5 to get 24.

$$6s^{2}=24$$

Divide both sides by 6.

$$s^{2}=\frac{24}{6}$$

Divide 24 by 6 to get 4.

$$s^{2}=4$$

Take the square root of both sides of the equation.

$$s=2 s=-2$$

Steps Using the Quadratic Formula

Subtract 19 from both sides.

$$6s^{2}-5-19=0$$

Subtract 19 from -5 to get -24.

$$6s^{2}-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s=\frac{0±\sqrt{0^{2}-4\times 6\left(-24\right)}}{2\times 6}$$

Square 0.

$$s=\frac{0±\sqrt{-4\times 6\left(-24\right)}}{2\times 6}$$

Multiply -4 times 6.

$$s=\frac{0±\sqrt{-24\left(-24\right)}}{2\times 6}$$

Multiply -24 times -24.

$$s=\frac{0±\sqrt{576}}{2\times 6}$$

Take the square root of 576.

$$s=\frac{0±24}{2\times 6}$$

Multiply 2 times 6.

$$s=\frac{0±24}{12}$$

Now solve the equation s=\frac{0±24}{12} when ± is plus. Divide 24 by 12.

$$s=2$$

Now solve the equation s=\frac{0±24}{12} when ± is minus. Divide -24 by 12.

$$s=-2$$

The equation is now solved.

$$s=2 s=-2$$