Question

Solve the quadratic equation x^2 + 5x - 6 = 0 and provide the solutions in the form of an ordered pair.

Answer 1

To solve the quadratic equation \( x^2 + 5x - 6 = 0 \), we can use the quadratic formula:

\[
x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}
\]

In the equation \( ax^2 + bx + c = 0 \), we have \( a = 1 \), \( b = 5 \), and \( c = -6 \).

First, we need to calculate the discriminant:

\[
b^2 - 4ac = 5^2 - 4(1)(-6) = 25 + 24 = 49
\]

Now we can substitute the values into the quadratic formula:

\[
x = \frac{{-5 \pm \sqrt{49}}}{2(1)} = \frac{{-5 \pm 7}}{2}
\]

Now we calculate the two potential solutions:

1. Using the positive square root:

\[
x = \frac{{-5 + 7}}{2} = \frac{2}{2} = 1
\]

2. Using the negative square root:

\[
x = \frac{{-5 - 7}}{2} = \frac{{-12}}{2} = -6
\]

Thus, the two solutions are \( x = 1 \) and \( x = -6 \).

Therefore, in the form of an ordered pair, the solutions are:

\[
(1, -6)
\]