Let's solve the given equation step-by-step:
1. Given Equation:
[tex]\[
x^2 - 10x = 14
\][/tex]
2. Rearrange to Standard Form:
[tex]\[
x^2 - 10x - 14 = 0
\][/tex]
3. Completing the Square:
To complete the square for the expression [tex]\( x^2 - 10x \)[/tex]:
a. Take the coefficient of [tex]\(x\)[/tex], which is -10, divide by 2, and square it:
[tex]\[
\left(\frac{-10}{2}\right)^2 = (-5)^2 = 25
\][/tex]
b. Add and subtract this squared term inside the equation:
[tex]\[
x^2 - 10x + 25 - 25 - 14 = 0
\][/tex]
[tex]\[
(x - 5)^2 - 25 - 14 = 0
\][/tex]
Simplify:
[tex]\[
(x - 5)^2 - 39 = 0
\][/tex]
4. Equivalent Equation:
Move the constant term to the other side of the equation:
[tex]\[
(x - 5)^2 = 39
\][/tex]
Thus, the equation equivalent to the given equation [tex]\(x^2 - 10x = 14\)[/tex] is:
[tex]\[
(x - 5)^2 = 39
\][/tex]
Among the provided options, the correct answer is:
[tex]\[
(x - 5)^2 = 39
\][/tex]
