Question

values of x by factoring.

$x^2 + 2x - 9 = 2x$

attempt 1 out of 2

Explanation:

Step1: Simplify the equation

Subtract \(2x\) from both sides of the equation \(x^{2}+2x - 9=2x\) to get it in standard quadratic form.
\(x^{2}+2x-2x - 9=2x - 2x\)
Simplifying both sides, we have \(x^{2}-9 = 0\)

Step2: Factor the quadratic expression

Notice that \(x^{2}-9\) is a difference of squares, which can be factored using the formula \(a^{2}-b^{2}=(a + b)(a - b)\). Here, \(a=x\) and \(b = 3\) (since \(9=3^{2}\)). So, \(x^{2}-9=(x + 3)(x - 3)=0\)

Step3: Solve for \(x\)

Set each factor equal to zero and solve for \(x\):

• For \(x+3=0\), subtract 3 from both sides: \(x=-3\)
• For \(x - 3=0\), add 3 to both sides: \(x = 3\)

Answer:

The values of \(x\) are \(x=-3\) and \(x = 3\)