Lesson 7

Noah solved the equation \(5x^2=45\). Here are his steps:

Find the solution(s) to each equation, or explain why there is no solution.

1. \(\sqrt{x+4}+7=5\)
2. \(\sqrt{47-x}-2 = 4\)
3. \(\frac12 \sqrt{20+x} = 5\)

Which is a solution to the equation \(\sqrt{5-x}+13=4\)?

86

81

9

The equation has no solution.

Select all expressions that are equal to \(\frac{1}{(\sqrt2)^5}\).

\(\text- \frac{5}{\sqrt2}\)

\(\frac{1}{\sqrt{2^5}}\)

\(\frac{1}{\sqrt{32}}\)

\(\text- (\sqrt2)^5\)

\(\text- 2^{\frac52}\)

\(2^{\text- \frac52}\)

Which are the solutions to the equation \(x^2=36\)?

6 only

-6 only

6 and -6

This equation has no solutions.

Here is a graph of \(y=x^2\).

1. Use the graph to estimate all solutions to the equation \(x^2=3\).
2. If you square your estimates, what number should they be close to?
3. Square your estimates. How close did you get to this number?

The polynomial function \(q(x)=3x^3+11x^2-14x-40\) has a known factor of \((3x + 5)\). Rewrite \(q(x)\) as the product of linear factors.