Solve for $u$ . $\newline$ $7u^2 + 13u - 2 = 0$ $\newline$ Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. $\newline$ $u = \_\_$

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Algebra 2

Solve polynomial equations

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Q. Solve for

u

\newline

7u^2 + 13u - 2 = 0

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

u = \_\_

Find Numbers: Find two numbers that multiply to $a \times c$ ( $7 \times -2 = -14$ ) and add up to $b$ ( $13$ ).
Apply Numbers: The numbers that work are $14$ and $-1$ because $14 \times -1 = -14$ and $14 + (-1) = 13$ .
Rewrite Middle Term: Rewrite the middle term using the numbers found in Step $2$ : $7u^2 + 14u - u - 2$ .
Factor by Grouping: Factor by grouping: $(7u^2 + 14u) + (-u - 2)$ .
Factor Common Terms: Factor out the common terms: $7u(u + 2) - 1(u + 2)$ .
Factor Common Binomial: Factor out the common binomial: $(7u - 1)(u + 2)$ .
Set Equal to Zero: Set each factor equal to zero: $7u - 1 = 0$ and $u + 2 = 0$ .
Solve for u: Solve for u from the first equation: $7u = 1$ ; $u = \frac{1}{7}.$
Solve for u: Solve for u from the first equation: $7u = 1$ ; $u = \frac{1}{7}$ .Solve for u from the second equation: $u = -2$ .