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olchik [2.2K]
3 years ago
11

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

Mathematics
1 answer:
asambeis [7]3 years ago
6 0
We do completing the square as follows:

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

2. Factor out the coefficient of the x^2 term.
</span>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
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