SOLUTION: sqrt(2x+5)=x-5

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Question 212144: sqrt(2x+5)=x-5
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x in the following equation

sqrt%282x%2B5%29=x-5

Step 1. Square Both Sides of Equation

%28sqrt%282x%2B5%29%29%5E2=%28x-5%29%5E2

2x%2B5=x%5E2-10x%2B25

Step 2. Simplify to get a quadratic equation. Subtract 2x+5 from both sides of equation

2x%2B5-%282x%2B5%29=%28x-5%29%5E2=x%5E2-10x%2B25-%282x%2B5%29

0=x%5E2-10x%2B25-%282x%2B5%29

0=x%5E2-8x%2B20

Step 3. Now use the quadratic equation

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=1, b=-8 and c=20 and follow steps below:

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-3+=+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=%28-2%29%5E2-4%2A1%2A-3=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+3
x%5B2%5D+=+%28-%28-2%29-sqrt%28+16+%29%29%2F2%5C1+=+-1

Quadratic expression 1x%5E2%2B-2x%2B-3 can be factored:
1x%5E2%2B-2x%2B-3+=+1%28x-3%29%2A%28x--1%29
Again, the answer is: 3, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-3+%29



Step 4. x=3 and x=-1 are solutions to the equation.

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