Question

Solve x2 − 7x = −13.

x equals quantity of negative 7 plus or minus I square root of 6 all over 2
x equals quantity of negative 7 plus or minus I square root of 3 all over 2
x equals quantity of 7 plus or minus I square root of 6 all over 2
x equals quantity of 7 plus or minus I square root of 3 all over 2

Answer 1

To solve the equation \( x^2 - 7x = -13 \), we first rearrange it into standard form:

\[
x^2 - 7x + 13 = 0
\]

Next, we apply the quadratic formula:

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

In this case, \( a = 1 \), \( b = -7 \), and \( c = 13 \). Plugging in these values:

1. Calculate the discriminant (\( b^2 - 4ac \)):
\[
(-7)^2 - 4 \cdot 1 \cdot 13 = 49 - 52 = -3
\]

2. Since the discriminant is negative, the solutions will involve imaginary numbers.

3. Substitute \( a \), \( b \), and the calculated discriminant into the quadratic formula:
\[
x = \frac{-(-7) \pm \sqrt{-3}}{2 \cdot 1} = \frac{7 \pm \sqrt{-3}}{2}
\]
\[
= \frac{7 \pm i\sqrt{3}}{2}
\]

Thus, the solutions for the equation \( x^2 - 7x + 13 = 0 \) are:

\[
x = \frac{7 \pm i\sqrt{3}}{2}
\]

Out of the options provided, the correct solution is:
\[
x = \frac{7 + \pm i\sqrt{3}}{2}
\]