Question

X squared + 20x = 69

Answer 1

To solve the equation \( x^2 + 20x = 69 \), we first rearrange it into standard quadratic form:

\[
x^2 + 20x - 69 = 0
\]

Next, we can use the quadratic formula to find the values of \( x \):

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

Here, \( a = 1 \), \( b = 20 \), and \( c = -69 \).

Let's calculate the discriminant \( b^2 - 4ac \):

\[
b^2 = 20^2 = 400
\]
\[
4ac = 4 \times 1 \times (-69) = -276
\]
\[
b^2 - 4ac = 400 - (-276) = 400 + 276 = 676
\]

Now we can find the roots:

\[
x = \frac{-20 \pm \sqrt{676}}{2 \times 1}
\]
\[
\sqrt{676} = 26
\]
\[
x = \frac{-20 \pm 26}{2}
\]

Now we can calculate the two possible values for \( x \):

1. For the plus sign:
\[
x = \frac{-20 + 26}{2} = \frac{6}{2} = 3
\]

2. For the minus sign:
\[
x = \frac{-20 - 26}{2} = \frac{-46}{2} = -23
\]

Thus, the solutions to the equation \( x^2 + 20x = 69 \) are:

\[
x = 3 \quad \text{and} \quad x = -23
\]