Solve: (8-u)(5u-7) = 0
Answer
u = 1.4 or u = 8
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Step-by-Step Breakdown
- Expand and simplify the left-hand side: (8-u)(5u-7) = -5u^2 + 47u - 56
- Expand and simplify the right-hand side: 0 = 0
- Move every term to one side so the equation reads "...= 0": -5u^2 + 47u - 56 = 0
- This is a quadratic equation of the form au^2+bu+c=0, with a=-5, b=47, c=-56.
- Compute the discriminant: D = b^2-4ac = (47)^2 - 4(-5)(-56) = 1089
- D > 0, so there are two real solutions: u = (-b ± √D) / (2a) = (1.4, 8)
Theory & Definitions
A quadratic equation au^2+bu+c=0 (a≠0) is solved with the quadratic formula: u = (-b ± √(b^2-4ac)) / (2a). The discriminant D=b^2-4ac tells you how many real solutions exist: two when D>0, one repeated solution when D=0, and two complex solutions when D<0.
Frequently Asked Questions
What is the solution to (8-u)(5u-7) = 0?
u = 1.4 or u = 8.