Solve Quadratic Equations Using the Square Root Property: example 10.13

Solve: $4 n^{2} + 4 n + 1 = 16$ .

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve: $9 m^{2} - 12 m + 4 = 25$ .

How did it go?

		$4 n^{2} + 4 n + 1 = 16$
Factor the perfect square trinomial.		${(2 n + 1)}^{2} = 16$
Use the Square Root Property.		$2 n + 1 = \pm \sqrt{16}$
Simplify the radical.		$2 n + 1 = \pm 4$
Solve for n.		$2 n = − 1 \pm 4$
Divide each side by 2.		$\begin{matrix} \frac{2 n}{2} & = & \frac{- 1 \pm 4}{2} \\ n & = & \frac{- 1 \pm 4}{2} \end{matrix}$
Rewrite to show two solutions.		$n = \frac{- 1 + 4}{2}, n = \frac{- 1 - 4}{2}$
Simplify each equation.		$n = \frac{3}{2}, n = - \frac{5}{2}$
Check.

		$4 n^{2} + 4 n + 1 = 16$
Factor the perfect square trinomial.		${(2 n + 1)}^{2} = 16$
Use the Square Root Property.		$2 n + 1 = \pm \sqrt{16}$
Simplify the radical.		$2 n + 1 = \pm 4$
Solve for n.		$2 n = − 1 \pm 4$
Divide each side by 2.		$\begin{matrix} \frac{2 n}{2} & = & \frac{- 1 \pm 4}{2} \\ n & = & \frac{- 1 \pm 4}{2} \end{matrix}$
Rewrite to show two solutions.		$n = \frac{- 1 + 4}{2}, n = \frac{- 1 - 4}{2}$
Simplify each equation.		$n = \frac{3}{2}, n = - \frac{5}{2}$
Check.