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

Move Terms to One Side: Move all terms to one side of the equation to set it equal to zero. x^2 - 5x + 2x = 0 Combine like terms. x^2 - 3x = 0Factor Out Common Term: Factor out the common term x from the left side of the equation. x(x - 3) = 0Apply Zero-Product Property: 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. Set each factor equal to zero and solve for x. x = 0 or x - 3 = 0Solve for x: Solve for x in the second equation. x - 3 = 0 Add 3 to both sides. x = 3

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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=-2 x

\newline

Answer:

x=

Move Terms to One Side: Move all terms to one side of the equation to set it equal to zero. $\newline$ $x^2 - 5x + 2x = 0$ $\newline$ Combine like terms. $\newline$ $x^2 - 3x = 0$
Factor Out Common Term: Factor out the common term $x$ from the left side of the equation. $x(x - 3) = 0$
Apply Zero-Product Property: 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. $\newline$ Set each factor equal to zero and solve for $x$ . $\newline$ $x = 0$ or $x - 3 = 0$
Solve for x: Solve for x in the second equation. $\newline$ $x - 3 = 0$ $\newline$ Add $3$ to both sides. $\newline$ $x = 3$