Question

Solve the equation for x, where x is a real number (5 points):
-3x^2 + 2x - 26 = -34

Answer 1

Add 34 to both sides to the equation becomes -3x^2 + 2x + 8 = 0.

To solve this equation, we can use the quadratic formula. The quadratic formula solves equations of the form ax^2 + bx + c = 0
x = [ -b ± √(b^2 - 4ac) ] / (2a)
x = [ -2 ± √(2^2 - 4(-3)(8)) ] / ( 2(-3) )
x = [ -2 ± √(4 - (-96) ) ] / ( -6 )
x = [ -2 ± √(100) ] / ( -6)
x = [ -2 ± 10 ] / ( -6 )
x = 1/3 ± -5/3
The answers are 1/3 + 5/3 = 2 and 1/3 - 5/3 = -4/3.

Answer 2

Subtract the left side, then factor.
0 = 3x^2 -2x -8
(x-2)(3x+4) = 0
The solutions are those values of x that make the factors zero.

x = 2, -4/3