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

jbouyer Jan 28, 2019

#1**+1 **

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

Mclovin123 Jan 28, 2019

#2**+1 **

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

CPhill Jan 28, 2019