Question

Solve the equation for x, where x is a real number (5 points):
-7x^2 + 23x - 25 = -24

Answer 1

Add 24 to both sides so that the equation becomes -7x^2 + 23x - 1 = 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 = [ -23 ± √(23^2 - 4(-7)(-1)) ] / ( 2(-7) )
x = [ -23 ± √(529 - (28) ) ] / ( -14 )
x = [ -23 ± √(501) ] / ( -14)
x = [ -23 ± sqrt(501) ] / ( -14 )
x = 23/14 ± -sqrt(501)/14
The answers are 23/14 + sqrt(501)/14 and 23/14 - sqrt(501)/14.

Answer 2

Subtract the left side, then use the quadratic formula.
7x^2 -23x +1 = 0
x = (-(-23) ±√((-23)^2 -4(7)(1)))/(2(7))
x = (23 ±√501)/14 ≈ {0.0440693, 3.241645}