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Solve for $u$ . $\newline$ $u^2 - 41u = 0$ $\newline$ 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

u^2 - 41u = 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 out common factor: Factor out the common factor $u$ . We notice that both terms in the equation $u^2 - 41u$ have a common factor of $u$ . We can factor out $u$ from both terms to simplify the equation. $u(u - 41) = 0$
Set factors equal to zero: Set each factor equal to zero. $\newline$ Since the product of two factors is zero, at least one of the factors must be zero. We set each factor equal to zero and solve for $u$ . $\newline$ $u = 0$ or $u - 41 = 0$
Solve for u: Solve for $u$ when $u - 41 = 0$ . To find the second solution, we add $41$ to both sides of the equation $u - 41 = 0$ . $u - 41 + 41 = 0 + 41$ $u = 41$

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