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

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

Jan 28, 2019

#1
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1. Put all terms with variable on one side and the constants on the other side.5x^2 - 3x = 252.

Factor out the coefficient of the x^2 term

.5(x^2 - 3x/5) = 253.

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 + 9/204.

We simplify as follows:

5(x^2 - 3x/5 + 9/100) = 25 + 9/205(x - 3/10)^2 = 509/20(x - 3/10)^2 = 509/100x1 = √(509) /100 + 3/10x2  = -√(509) /100 + 3/10

Jan 28, 2019
#2
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Thanks, Mclovin.....here's another way...

5x ^2 - 3x = 25     divide through by 5

x^2  - (3/5)x  =  5

Take (1/2) of (3/5) = 3/10....square it = 9/100.....add to both sides

x^2 - (3/5)x + 9/100 =  5 + 9/100      factor the right side

(x - 3/10)^2 =   509/100    take both roots

x - 3/10 =  ±√ [509/100]

x - 3/10 = ±√(509) /10     add 3/10 to both sides

x =     [ 3 ±√509 ] / 10

Jan 28, 2019