Solve Quadratic Equations Using the Square Root Property: example 10.5

Solve: $\frac{2}{3} u^{2} + 5 = 17$ .

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: $\frac{1}{2} x^{2} + 4 = 24$ .

How did it go?

		$\frac{2}{3} u^{2} + 5 = 17$
Isolate the quadratic term.		$\frac{2}{3} u^{2} = 12$
Multiply by $\frac{3}{2}$ to make the coefficient 1.		$\frac{3}{2} \cdot \frac{2}{3} u^{2} = \frac{3}{2} \cdot 12$
Simplify.		$u^{2} = 18$
Use the Square Root Property.		$u = \pm \sqrt{18}$
Simplify the radical.		$u = \pm \sqrt{9} \sqrt{2}$
Simplify.		$u = \pm 3 \sqrt{2}$
Rewrite to show two solutions.		$u = 3 \sqrt{2}, u = − 3 \sqrt{2}$
Check.

		$\frac{2}{3} u^{2} + 5 = 17$
Isolate the quadratic term.		$\frac{2}{3} u^{2} = 12$
Multiply by $\frac{3}{2}$ to make the coefficient 1.		$\frac{3}{2} \cdot \frac{2}{3} u^{2} = \frac{3}{2} \cdot 12$
Simplify.		$u^{2} = 18$
Use the Square Root Property.		$u = \pm \sqrt{18}$
Simplify the radical.		$u = \pm \sqrt{9} \sqrt{2}$
Simplify.		$u = \pm 3 \sqrt{2}$
Rewrite to show two solutions.		$u = 3 \sqrt{2}, u = − 3 \sqrt{2}$
Check.