SOLUTION: Use algrebra so solve (x-1)(x+2)=18 iv tried and failed please help me :)

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Question 226036: Use algrebra so solve (x-1)(x+2)=18
iv tried and failed please help me :)
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Use algebra so solve (x-1)(x+2)=18

Step 1. Multiply out to get rid of the parenthesis.

%28x-1%29%28x%2B2%29=x%5E2%2B2x-x-2=18

x%5E2%2Bx-2=18

Step 2. Subtract 18 from both sides of the equation

x%5E2%2Bx-2-18=18-18

x%5E2%2Bx-20=0

and x-4=0 or x=-5 and x=4

Step 4. We can also solve using the quadratic equation shown below:

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

where a=1, b=1 and c=-20

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-20+=+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=%281%29%5E2-4%2A1%2A-20=81.

Discriminant d=81 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+81+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+81+%29%29%2F2%5C1+=+4
x%5B2%5D+=+%28-%281%29-sqrt%28+81+%29%29%2F2%5C1+=+-5

Quadratic expression 1x%5E2%2B1x%2B-20 can be factored:
1x%5E2%2B1x%2B-20+=+1%28x-4%29%2A%28x--5%29
Again, the answer is: 4, -5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-20+%29



...same as before.

Step 5. ANSWER: The solutions are x=-5 and x=4.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J