Solve for all values of x by factoring. x^(2)-3x-5=-3x-1 Answer: x=

Simplify Equation: Simplify the equation by moving all terms to one side to set the equation to zero. x^2 - 3x - 5 = -3x - 1 Add 3x and 1 to both sides of the equation: x^2 - 3x + 3x - 5 + 1 = 0 x^2 - 4 = 0Factor Quadratic: Factor the simplified quadratic equation. We notice that x^2 - 4 is a difference of squares, which can be factored as: (x - 2)(x + 2) = 0Solve for x: Solve for x by setting each factor equal to zero. First factor: x - 2 = 0 Add 2 to both sides: x = 2 Second factor: x + 2 = 0 Subtract 2 from both sides: x = -2

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Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Solve for all values of

x

by factoring.

\newline

x^{2}-3 x-5=-3 x-1

\newline

Answer:

x=

Simplify Equation: Simplify the equation by moving all terms to one side to set the equation to zero. $\newline$ $x^2 - 3x - 5 = -3x - 1$ $\newline$ Add $3x$ and $1$ to both sides of the equation: $\newline$ $x^2 - 3x + 3x - 5 + 1 = 0$ $\newline$ $x^2 - 4 = 0$
Factor Quadratic: Factor the simplified quadratic equation. $\newline$ We notice that $x^2 - 4$ is a difference of squares, which can be factored as: $\newline$ $(x - 2)(x + 2) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ First factor: $x - 2 = 0$ $\newline$ Add $2$ to both sides: $\newline$ $x = 2$ $\newline$ Second factor: $x + 2 = 0$ $\newline$ Subtract $2$ from both sides: $\newline$ $x = -2$