Question

Explain how to solve 5x^2 - 3x = 25 by completing the square. What are the solutions?

Answer 1

We do completing the square as follows:

1. Put all terms with variable on one side and the constants on the other side.
5x^2 - 3x = 25

2. Factor out the coefficient of the x^2 term.
5(x^2 - 3x/5) = 25

3. Inside the parentheses, we add a number that would complete the square and also add this to the other side of the equation. In this case we add 9/100 and on the other  side we add 9/20.
5(x^2 - 3x/5 + 9/100) = 25 + 9/20

4. We simplify as follows:
5(x^2 - 3x/5 + 9/100) = 25 + 9/20
5(x - 3/10)^2 = 509/20
(x - 3/10)^2 = 509/100

x1 = √(509) /100 + 3/10
x2  = -√(509) /100 + 3/10