Question

X^2 +5x -6= 0 by factoring

Answer 1

To solve the quadratic equation \( x^2 + 5x - 6 = 0 \) by factoring, we need to express the quadratic in the form of \((x + p)(x + q) = 0\), where \(p\) and \(q\) are numbers that add up to the coefficient of the \(x\) term (which is 5) and multiply to the constant term (which is -6).

1. We need two numbers that multiply to \(-6\) and add to \(5\).

The numbers that fit this are \(6\) and \(-1\) because:
- \(6 \times -1 = -6\)
- \(6 + (-1) = 5\)

2. Now, we can rewrite the quadratic equation:
\[
x^2 + 6x - x - 6 = 0
\]

3. Next, group the terms:
\[
(x^2 + 6x) + (-x - 6) = 0
\]

4. Factor by grouping:
\[
x(x + 6) - 1(x + 6) = 0
\]

5. Factor out the common term:
\[
(x + 6)(x - 1) = 0
\]

6. Now, set each factor to zero:
\[
x + 6 = 0 \quad \Rightarrow \quad x = -6
\]
\[
x - 1 = 0 \quad \Rightarrow \quad x = 1
\]

So, the solutions to the equation \( x^2 + 5x - 6 = 0 \) are:
\[
x = -6 \quad \text{and} \quad x = 1
\]