SOLUTION: Solve: a: (2x + 3)^2 = 5 b: 2(x - 5)^2 = 3 (mark answers a and b)

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Question 184470: Solve:
a: (2x + 3)^2 = 5
b: 2(x - 5)^2 = 3
(mark answers a and b)
Answer by kailuen(7) About Me  (Show Source):
You can put this solution on YOUR website!
(2x + 3)^2 = 5
4x^2+12x+9-5=0
4x^2+12x+4=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B12x%2B4+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2812%29%5E2-4%2A4%2A4=80.

Discriminant d=80 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+80+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+80+%29%29%2F2%5C4+=+-0.381966011250105
x%5B2%5D+=+%28-%2812%29-sqrt%28+80+%29%29%2F2%5C4+=+-2.61803398874989

Quadratic expression 4x%5E2%2B12x%2B4 can be factored:
4x%5E2%2B12x%2B4+=+4%28x--0.381966011250105%29%2A%28x--2.61803398874989%29
Again, the answer is: -0.381966011250105, -2.61803398874989. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B12%2Ax%2B4+%29

x=-2.6, x= -0.38

2(x - 5)^2 = 3
2(x^2-10x+25)=3
2x^2-20x+47=0
x=3.775
x=6.224