Solve for all values of x by factoring. x^(2)-5x=-3x Answer: x=

Combine like terms: First, we need to bring all terms to one side of the equation to set it equal to zero. x^2 - 5x + 3x = 0 Combine like terms. x^2 - 2x = 0Factor the equation: Now, we factor the left side of the equation. We can factor out an x from each term. x(x - 2) = 0Apply zero product property: Next, we apply the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero. So, we set each factor equal to zero and solve for x. x = 0 or x - 2 = 0Solve for x: Solving the first equation: x = 0Check solutions: Solving the second equation: x - 2 = 0 x = 2

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Solve for all values of

x

by factoring.

\newline

x^{2}-5 x=-3 x

\newline

Answer:

x=

Combine like terms: First, we need to bring all terms to one side of the equation to set it equal to zero. $\newline$ $x^2 - 5x + 3x = 0$ $\newline$ Combine like terms. $\newline$ $x^2 - 2x = 0$
Factor the equation: Now, we factor the left side of the equation. $\newline$ We can factor out an $x$ from each term. $\newline$ $x(x - 2) = 0$
Apply zero product property: Next, we apply the zero product property, which states that if a product of two factors is $0$ , then at least one of the factors must be $0$ . So, we set each factor equal to $0$ and solve for $x$ . $x = 0$ or $x - 2 = 0$
Solve for x: Solving the first equation: $\newline$ $x = 0$
Check solutions: Solving the second equation: $\newline$ $x - 2 = 0$ $\newline$ $x = 2$