91Ó°ÊÓ

Determine whether each statement is true or false If the statement is false, make the necessary change(s) to produce a true statement. The equation \((x+5)^{2}=8\) is equivalent to \(x+5=2 \sqrt{2}\).

Determine whether each statement is true or false If the statement is false, make the necessary change(s) to produce a true statement. The equation \(x^{2}=-1\) has no solutions that are real numbers.

Determine whether each statement is true or false If the statement is false, make the necessary change(s) to produce a true statement. The solutions of \(3 x^{2}-5=0\) are \(\frac{\sqrt{5}}{3}\) and \(-\frac{\sqrt{5}}{3}\)

Find the value(s) of \(x\) if the distance between \((-3,-2)\) and \((x,-5)\) is 5 units.

Use a graphing utility to solve \(4-(x+1)^{2}=0 .\) Graph \(y=4-(x+1)^{2}\) in a \([-5,5,1]\) by \([-5,5,1]\) viewing rectangle. The equation's solutions are the graph's \(x\) -intercepts. Check by substitution in the given equation.

Use a graphing utility to solve \((x-1)^{2}-9=0\) Graph \(y=(x-1)^{2}-9\) in a \([-5,5,1]\) by \([-9,3,1]\) viewing rectangle. The equation's solutions are the graph's \(x\) -intercepts. Check by substitution in the given equation.

Factor completely: \(12 x^{2}+14 x-6\) (Section 6.5, Example 2)

$$\text { Divide: } \frac{x^{2}-x-6}{3 x-3} \div \frac{x^{2}-4}{x-1}$$

Solve: \(4(x-5)=22+2(6 x+3)\) (Section \(2.3,\) Example 3 )

Will help you prepare for the material covered in the next section. $$\text { Factor: } x^{2}+8 x+16$$