9.2.5 Practice

For questions 1 - 5, the standard form of an equation is $a{x}^2+bx+c$. For each expression, find the missing constant $c$ that would make the expression a perfect square.

For each equation in questions 11 - 14, use the following scenario.

Jada looks at Mai's work and is confused. She doesn't see how Mai got her answer.

Complete Mai's missing steps by answering the questions to help Jada see how Mai solved the equation.

$x^2+12x=13$

Step 1 - $x^2+12x+$ $\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}$ $=13+$ $\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}$

Step 2 - $(x+6{)}^2=49$

Step 3 - $\sqrt{(x+6{)}^2}=\sqrt{49}$

Step 4 - $x+6=\pm <!--\; \pm \; -->$ $\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}$

Step 5 - $x+6=$ $\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}$

Step 6 - $x+6=$ $-<!--\; -\; -->$ $\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}\mathrm{\_<!--\; \_\; -->}$

$x=1$ or $x=-<!--\; -\; -->13$

For questions 15 - 20, solve choose the equivalent equation with a perfect square on one side.

For questions 21-23, solve each equation by completing the square, then choose the two roots.

21. $x^2-6x+5=12$