To solve the equation \( x^2 + 6x = 40 \), we start by rearranging it into standard form:
\[ x^2 + 6x - 40 = 0 \]
Next, we can apply the quadratic formula, which is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In this case, \( a = 1 \), \( b = 6 \), and \( c = -40 \).
First, we calculate the discriminant:
\[ b^2 - 4ac = 6^2 - 4(1)(-40) = 36 + 160 = 196 \]
Next, we calculate the square root of the discriminant:
\[ \sqrt{196} = 14 \]
Now, we can substitute back into the quadratic formula:
\[ x = \frac{-6 \pm 14}{2(1)} \]
This gives us two possible solutions:
- Using the plus sign:
\[ x = \frac{-6 + 14}{2} = \frac{8}{2} = 4 \]
- Using the minus sign:
\[ x = \frac{-6 - 14}{2} = \frac{-20}{2} = -10 \]
Thus, the solutions to the equation \( x^2 + 6x = 40 \) are:
\[ x = -10 \quad \text{and} \quad x = 4 \]
The correct answer is:
x = −10 and x = 4