Solve for all values of x by factoring. x^(2)-6=3 Answer: x=

Move to Standard Form: Write the equation in standard form by moving all terms to one side. We start with the equation x^2 - 6 = 3 and move the constant term on the right side to the left side to get x^2 - 6 - 3 = 0. Now the equation is x^2 - 9 = 0.Factor Quadratic Equation: Factor the quadratic equation. We need to factor x^2 - 9. This is a difference of squares, which can be factored into (x + 3)(x - 3) = 0.Apply Zero Product Property: Solve for x using the zero product property. The zero product property states that if a product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x. x + 3 = 0 or x - 3 = 0.Solve for x: Solve each equation for x. For x + 3 = 0, we subtract 3 from both sides to get x = -3. For x - 3 = 0, we add 3 to both sides to get x = 3.

Home

Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Solve for all values of

x

by factoring.

\newline

x^{2}-6=3

\newline

Answer:

x=

Move to Standard Form: Write the equation in standard form by moving all terms to one side. $\newline$ We start with the equation $x^2 - 6 = 3$ and move the constant term on the right side to the left side to get $x^2 - 6 - 3 = 0$ . $\newline$ Now the equation is $x^2 - 9 = 0$ .
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ We need to factor $x^2 - 9$ . This is a difference of squares, which can be factored into $(x + 3)(x - 3) = 0$ .
Apply Zero Product Property: Solve for $x$ using the zero product property. $\newline$ The zero product property states that if a product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for $x$ . $\newline$ $x + 3 = 0$ or $x - 3 = 0$ .
Solve for x: Solve each equation for x. $\newline$ For $x + 3 = 0$ , we subtract $3$ from both sides to get $x = -3$ . $\newline$ For $x - 3 = 0$ , we add $3$ to both sides to get $x = 3$ .