Question

solving quadratics by factoring
score: 3/15 penalty: 1 off
question
solve for all values of x by factoring.
x² - 14 = -5
answer attempt 1 out of 2
+ additional solution ⊖ no solution
x =
submit answer

Explanation:

Step1: Rearrange the equation

First, we need to get the quadratic equation in standard form \(ax^2 + bx + c = 0\). Start with the given equation \(x^2 - 14 = -5\). Add 5 to both sides to isolate the quadratic terms and constants:
\(x^2 - 14 + 5 = 0\)
Simplify the constants:
\(x^2 - 9 = 0\)

Step2: Factor the quadratic

Notice that \(x^2 - 9\) is a difference of squares, which factors as \(a^2 - b^2 = (a - b)(a + b)\). Here, \(a = x\) and \(b = 3\) (since \(3^2 = 9\)), so:
\(x^2 - 9 = (x - 3)(x + 3) = 0\)

Step3: Solve for \(x\)

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

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

Answer:

\(x = 3\) or \(x = -3\) (or in boxed form, if needed, but as per instructions, we present the solutions clearly. If we were to box each, it would be \(\boxed{3}\) and \(\boxed{-3}\), but since the problem allows multiple solutions, we list both.)