Let's solve the quadratic equation step-by-step.
The given equation is:
[tex]\[ x^2 - 10x = -34 \][/tex]
First, we rewrite the equation in standard quadratic form [tex]\( ax^2 + bx + c = 0 \)[/tex]:
[tex]\[ x^2 - 10x + 34 = 0 \][/tex]
Now, we use the quadratic formula to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
For our equation [tex]\( x^2 - 10x + 34 = 0 \)[/tex], the coefficients are:
- [tex]\(a = 1\)[/tex]
- [tex]\(b = -10\)[/tex]
- [tex]\(c = 34\)[/tex]
Substituting these values into the quadratic formula, we get:
[tex]\[ x = \frac{-(-10) \pm \sqrt{(-10)^2 - 4 \cdot 1 \cdot 34}}{2 \cdot 1} \][/tex]
Simplifying inside the square root:
[tex]\[ x = \frac{10 \pm \sqrt{100 - 136}}{2} \][/tex]
[tex]\[ x = \frac{10 \pm \sqrt{-36}}{2} \][/tex]
[tex]\[ x = \frac{10 \pm 6i}{2} \][/tex]
Now, simplifying the fractions:
[tex]\[ x = 5 \pm 3i \][/tex]
Thus, the solutions to the quadratic equation [tex]\(x^2 - 10x = -34\)[/tex] are:
[tex]\[ x = 5 + 3i \quad \text{and} \quad x = 5 - 3i \][/tex]
The correct answer is:
B. [tex]\( x = 5 \pm 3i \)[/tex]
