Question
SOLVE BY FACTORING x^2+2x-35=0
Answers
GPT-4o mini
To solve the equation \(x^2 + 2x - 35 = 0\) by factoring, we need to find two numbers that multiply to \(-35\) (the constant term) and add to \(2\) (the coefficient of the linear term).
The two numbers that meet these criteria are \(7\) and \(-5\) because:
- \(7 \times -5 = -35\)
- \(7 + (-5) = 2\)
Now we can express the quadratic as a product of two binomials:
\[
(x + 7)(x - 5) = 0
\]
Next, we set each factor equal to zero:
1. \(x + 7 = 0\)
- \(x = -7\)
2. \(x - 5 = 0\)
- \(x = 5\)
Thus, the solutions to the equation \(x^2 + 2x - 35 = 0\) are:
\[
\boxed{-7} \quad \text{and} \quad \boxed{5}
\]
The two numbers that meet these criteria are \(7\) and \(-5\) because:
- \(7 \times -5 = -35\)
- \(7 + (-5) = 2\)
Now we can express the quadratic as a product of two binomials:
\[
(x + 7)(x - 5) = 0
\]
Next, we set each factor equal to zero:
1. \(x + 7 = 0\)
- \(x = -7\)
2. \(x - 5 = 0\)
- \(x = 5\)
Thus, the solutions to the equation \(x^2 + 2x - 35 = 0\) are:
\[
\boxed{-7} \quad \text{and} \quad \boxed{5}
\]