Solve for all values of x by factoring. x^(2)-9=0 Answer: x=

Set up equation: Set up the equation for factoring. We are given the equation x^2 - 9 = 0. This is a difference of squares because 9 is a perfect square (3^2).Factor difference of squares: Factor the difference of squares. The difference of squares can be factored as (a^2 - b^2) = (a + b)(a - b). In our case, a = x and b = 3, so we have: x^2 - 9 = (x + 3)(x - 3)Set factors equal: Set each factor equal to zero. Since the product of the factors is zero, we can set each factor equal to zero to find the values of x. x + 3 = 0 or x - 3 = 0Solve for x: Solve each equation for x. For the first equation: x + 3 = 0 x = -3 For the second equation: x - 3 = 0 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}-9=0

\newline

Answer:

x=

Set up equation: Set up the equation for factoring. $\newline$ We are given the equation $x^2 - 9 = 0$ . This is a difference of squares because $9$ is a perfect square ( $3^2$ ).
Factor difference of squares: Factor the difference of squares. $\newline$ The difference of squares can be factored as $(a^2 - b^2) = (a + b)(a - b)$ . In our case, $a = x$ and $b = 3$ , so we have: $\newline$ $x^2 - 9 = (x + 3)(x - 3)$
Set factors equal: Set each factor equal to zero. $\newline$ Since the product of the factors is zero, we can set each factor equal to zero to find the values of $x$ . $\newline$ $x + 3 = 0$ or $x - 3 = 0$
Solve for x: Solve each equation for x. $\newline$ For the first equation: $\newline$ $x + 3 = 0$ $\newline$ $x = -3$ $\newline$ For the second equation: $\newline$ $x - 3 = 0$ $\newline$ $x = 3$