SOLUTION: Solve the following equations for x using any method. 1) {{{ x^2-4x=2}}} Also for the equation: 2) {{{ abs(5-x)-4=2}}} would the correct answer be x=-1 or x=11?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve the following equations for x using any method. 1) {{{ x^2-4x=2}}} Also for the equation: 2) {{{ abs(5-x)-4=2}}} would the correct answer be x=-1 or x=11?       Log On


   

Question 623799: Solve the following equations for x using any method.
1) +x%5E2-4x=2
Also for the equation:
2) +abs%285-x%29-4=2
would the correct answer be x=-1 or x=11?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following equations for x using any method.
1) +x%5E2-4x=2
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B-2+=+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=%28-4%29%5E2-4%2A1%2A-2=24.

Discriminant d=24 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+24+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+24+%29%29%2F2%5C1+=+4.44948974278318
x%5B2%5D+=+%28-%28-4%29-sqrt%28+24+%29%29%2F2%5C1+=+-0.449489742783178

Quadratic expression 1x%5E2%2B-4x%2B-2 can be factored:
1x%5E2%2B-4x%2B-2+=+%28x-4.44948974278318%29%2A%28x--0.449489742783178%29
Again, the answer is: 4.44948974278318, -0.449489742783178. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-2+%29

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Also for the equation:
2) +abs%285-x%29-4=2
would the correct answer be x=-1 or x=11?
2) +abs%285-x%29-4=2
|x-5| = 6
x = 11
x = -1
is right.