Question

solve by factoring:

1. ( x^2 + 2x = 63 )

Explanation:

Step1: Rearrange the equation

First, we need to set the equation to standard quadratic form \(ax^2 + bx + c = 0\). So, subtract 63 from both sides of the equation \(x^2 + 2x = 63\).
We get \(x^2 + 2x - 63 = 0\).

Step2: Factor the quadratic

We need to find two numbers that multiply to -63 and add up to 2. Let's list the factor pairs of -63:

• 9 and -7: \(9\times(-7)= - 63\) and \(9+(-7)=2\).

So, we can factor the quadratic as \((x + 9)(x - 7)=0\).

Step3: Solve for x

Using the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\).
So, we set each factor equal to zero:

• For \(x + 9 = 0\), subtract 9 from both sides: \(x=-9\).
• For \(x - 7 = 0\), add 7 to both sides: \(x = 7\).

Answer:

\(x=-9\) or \(x = 7\)