Question

Solve for x in the equation 2 x squared + 3 x minus 7 = x squared + 5 x + 39.
x = negative 6 plus-or-minus StartRoot 82 EndRoot
x = negative 6 plus-or-minus 2 StartRoot 17 EndRoot
x = 1 plus-or-minus StartRoot 33 EndRoot
x = 1 plus-or-minus StartRoot 47 EndRoot

Answer 1

Start by bringing all terms to one side:
2x^2 + 3x - 7 - (x^2 + 5x + 39) = 0
⟹ x^2 - 2x - 46 = 0.

Use the quadratic formula: x = [2 ± sqrt((-2)^2 - 4·1·(-46))]/2 = [2 ± sqrt(188)]/2 = 1 ± sqrt(47).

So x = 1 ± √47 (the last choice).