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

Simplify Equation: Simplify the equation by adding 2 to both sides to set the equation to zero. x^2 - 3x - 2 + 2 = -2 + 2 x^2 - 3x = 0Factor Quadratic: Factor the simplified quadratic equation. We need to find two numbers that multiply to give 0 (the product of the constant term and the coefficient of x^2, which is 1) and add to give -3 (the coefficient of x). The numbers that satisfy these conditions are -3 and 0 because -3 * 0 = 0 and -3 + 0 = -3. Therefore, we can factor the equation as follows: x(x - 3) = 0Solve for x: Solve the factored equation for x. Set each factor equal to zero and solve for x: x = 0 or x - 3 = 0 If x - 3 = 0, then x = 3

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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-2=-2

\newline

Answer:

x=

Simplify Equation: Simplify the equation by adding $2$ to both sides to set the equation to zero. $\newline$ $x^2 - 3x - 2 + 2 = -2 + 2$ $\newline$ $x^2 - 3x = 0$
Factor Quadratic: Factor the simplified quadratic equation. $\newline$ We need to find two numbers that multiply to give $0$ (the product of the constant term and the coefficient of $x^2$ , which is $1$ ) and add to give $-3$ (the coefficient of $x$ ). $\newline$ The numbers that satisfy these conditions are $-3$ and $0$ because $-3 \times 0 = 0$ and $-3 + 0 = -3$ . $\newline$ Therefore, we can factor the equation as follows: $\newline$ $x(x - 3) = 0$
Solve for x: Solve the factored equation for x. $\newline$ Set each factor equal to zero and solve for x: $\newline$ $x = 0$ or $x - 3 = 0$ $\newline$ If $x - 3 = 0$ , then $x = 3$