Question 619621: x^2+3x=28. I need help to solve this problem by completing the square
Answer by lenny460(1073)   (Show Source):
You can put this solution on YOUR website! Completing the Square:
x^2 + 3x = 28
The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides.
Add 2.25 to each side of the equation.
x^2 + 3x + 2.25 = 28 + 2.25
Combine like terms:
28 + 2.25 = 30.25
Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 30.25
Calculate the square root of the right side = 5.5
The square root of 30.25 = 5.5
Break this problem into two subproblems by setting:
(x + 1.5) equal to 5.5 and -5.5
Subproblem 1
x + 1.5 = 5.5
Subtract 1.5 from each side of the equation.
x + 1.5 - 1.5 = 5.5 - 1.5
Combine like terms:
1.5 - 1.5 = 0
5.5 - 1.5 = 4
x = 4
Subproblem 2
x + 1.5 = -5.5
Subtract 1.5 from each side of the equation.
x + 1.5 - 1.5 = -5.5 - 1.5
Combine like terms:
1.5 - 1.5 = 0
-5.5 - 1.5 = -7
x = -7
Solution:
x = 4, -7
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