Solve L^2+3=19

$$L ^ { 2 } + 3 = 19$$

Solve for L

$$L=4$$

$$L=-4$$

Steps Using Difference of Squares

Subtract 19 from both sides.

$$L^{2}+3-19=0$$

Subtract 19 from 3 to get -16.

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

Consider L^{2}-16. Rewrite L^{2}-16 as L^{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).

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

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

$$L=4 L=-4$$

Steps by Finding Square Root

Subtract 3 from both sides.

$$L^{2}=19-3$$

Subtract 3 from 19 to get 16.

$$L^{2}=16$$

Take the square root of both sides of the equation.

$$L=4 L=-4$$

Steps Using the Quadratic Formula

Subtract 19 from both sides.

$$L^{2}+3-19=0$$

Subtract 19 from 3 to get -16.

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

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}.

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

Square 0.

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

Multiply -4 times -16.

$$L=\frac{0±\sqrt{64}}{2}$$

Take the square root of 64.

$$L=\frac{0±8}{2}$$

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

$$L=4$$

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

$$L=-4$$

The equation is now solved.

$$L=4 L=-4$$