Question

Solve the equation for x, where x is a real number (5 points): 2x^2 + 7x - 9 = -3

Answer 1

Add 3 to both sides so that the equation becomes 2x^2 + 7x - 6 = 0.
To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
                              x = [ -b ± √(b^2 - 4ac) ] / (2a)
                              x = [ -7 ± √(7^2 - 4(2)(-6)) ] / ( 2(2) )
                              x = [ -7 ± √(49 - (-48) ) ] / ( 4 )
                              x = [ -7 ± √(97) ] / ( 4)
                              x = [ -7 ± sqrt(97) ] / ( 4 )
                              x = -7/4 ± sqrt(97)/4
The answers are -7/4 + sqrt(97)/4 and -7/4 - sqrt(97)/4.