SOLUTION: x^2-4x+2 = 0 5x^2 - 2 = 2x 3x^2 - 6x = 2

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: x^2-4x+2 = 0 5x^2 - 2 = 2x 3x^2 - 6x = 2       Log On


   

Question 103618: x^2-4x+2 = 0
5x^2 - 2 = 2x
3x^2 - 6x = 2
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
1. x%5E2-4x%2B2+=+0+
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B2+=+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%2A2=8.

Discriminant d=8 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+8+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+8+%29%29%2F2%5C1+=+3.41421356237309
x%5B2%5D+=+%28-%28-4%29-sqrt%28+8+%29%29%2F2%5C1+=+0.585786437626905

Quadratic expression 1x%5E2%2B-4x%2B2 can be factored:
1x%5E2%2B-4x%2B2+=+1%28x-3.41421356237309%29%2A%28x-0.585786437626905%29
Again, the answer is: 3.41421356237309, 0.585786437626905. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B2+%29


2. 5x%5E2+-+2+=+2x+ => 5x%5E2+-2x+-2+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-2x%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=%28-2%29%5E2-4%2A5%2A-2=44.

Discriminant d=44 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+44+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+44+%29%29%2F2%5C5+=+0.86332495807108
x%5B2%5D+=+%28-%28-2%29-sqrt%28+44+%29%29%2F2%5C5+=+-0.46332495807108

Quadratic expression 5x%5E2%2B-2x%2B-2 can be factored:
5x%5E2%2B-2x%2B-2+=+5%28x-0.86332495807108%29%2A%28x--0.46332495807108%29
Again, the answer is: 0.86332495807108, -0.46332495807108. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-2%2Ax%2B-2+%29


3. 3x%5E2+-+6x+=+2 = > 3x%5E2+-+6x+-+2+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-6x%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=%28-6%29%5E2-4%2A3%2A-2=60.

Discriminant d=60 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+60+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+60+%29%29%2F2%5C3+=+2.29099444873581
x%5B2%5D+=+%28-%28-6%29-sqrt%28+60+%29%29%2F2%5C3+=+-0.290994448735806

Quadratic expression 3x%5E2%2B-6x%2B-2 can be factored:
3x%5E2%2B-6x%2B-2+=+3%28x-2.29099444873581%29%2A%28x--0.290994448735806%29
Again, the answer is: 2.29099444873581, -0.290994448735806. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-6%2Ax%2B-2+%29