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Solve for $u$ . $\newline$ $38u^2 + 39u = 0$ $\newline$ 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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Solve a quadratic equation by factoring

Full solution

Q. Solve for

u

.

\newline

38u^2 + 39u = 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 = \_\_\_

Factor GCF and Equate: Factor out the greatest common factor (GCF) from the equation $38u^2 + 39u = 0$ . The GCF of $38u^2$ and $39u$ is $u$ . Factor out $u$ from each term. $u(38u + 39) = 0$
Solve for u: Set each factor equal to zero and solve for u. $\newline$ First, set $u$ equal to zero: $\newline$ $u = 0$ $\newline$ This is one solution. $\newline$ Next, set the other factor equal to zero: $\newline$ $38u + 39 = 0$
Solve $38u + 39 = 0$ : Solve the equation $38u + 39 = 0$ for $u$ . $\newline$ Subtract $39$ from both sides of the equation to isolate the term with $u$ . $\newline$ $38u + 39 - 39 = 0 - 39$ $\newline$ $38u = -39$ $\newline$ Now, divide both sides by $38$ to solve for $u$ . $\newline$ $u = -\frac{39}{38}$
Final Solutions: Write the values of $u$ . $\newline$ We have found two solutions: $u = 0$ and $u = -\frac{39}{38}$ .

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