Solve for x in the 2x squared + 3x - 7 = x squared + 5x + 39

a. x = -6 plus-minus the square root of 82
b. x = -6 plus-minus 2 root 17
c. x = 1 plus-minus the root of 33
d. x = 1 plus-minus the root of 47

timed

The solution of the quadratic equation is:

d. x = 1 plus-minus the root of 47

The equation given is:

Passing everything to the same side, we have that:

Which is a quadratic equation with coefficients . Then:

Thus, the solution is:

d. x = 1 plus-minus the root of 47

A similar problem is given at link

D) x = 1 ± √(47)

Step-by-step explanation:

2x² + 3x - 7 = x² + 5x + 39

move all terms to one side:

x² - 2x - 46 = 0

complete the square:

x² - 2x + 1 - 1 - 46 = 0

(x - 1)² - 47 = 0

add 47 to both sides:

(x - 1)² = 47

square root both sides:

x - 1 = ±√(47)

add 1 to both sides:

x = 1 ± √(47)

the answer is 13 cm