SOLUTION: more w.s. problems yay! Solve by factoring {{{2x^2-11x+15=0}}} also {{{11x=3x^2}}} Solve these by the quadractic formula? (use simplest radical form) a. {{{x^2-2x-11=0}}} b.

Algebra ->  Square-cubic-other-roots -> SOLUTION: more w.s. problems yay! Solve by factoring {{{2x^2-11x+15=0}}} also {{{11x=3x^2}}} Solve these by the quadractic formula? (use simplest radical form) a. {{{x^2-2x-11=0}}} b.      Log On


   

Question 63418: more w.s. problems yay! Solve by factoring
2x%5E2-11x%2B15=0
also 11x=3x%5E2
Solve these by the quadractic formula? (use simplest radical form)
a. x%5E2-2x-11=0
b. 4x%5E2%2B4x=5
Answer by sarahschober(35) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2-11x%2B15=0= %28x-3%29%282x-5%29
11x=3x%5E2=x%283x-11%29
x%5E2-2x-11=0=
1%2B2sqrt%283%29and+1-2sqrt%283%29
see+more+below
4x%5E2%2B4x=5=
%28%281%2Bsqrt%286%29%29%2F2%29+and+%28%281-sqrt%286%29%29%2F2%29
see+more+below
x%5E2-2x-11=0=
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-11+=+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-11=48.

Discriminant d=48 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+48+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+48+%29%29%2F2%5C1+=+4.46410161513775
x%5B2%5D+=+%28-%28-2%29-sqrt%28+48+%29%29%2F2%5C1+=+-2.46410161513775

Quadratic expression 1x%5E2%2B-2x%2B-11 can be factored:
1x%5E2%2B-2x%2B-11+=+%28x-4.46410161513775%29%2A%28x--2.46410161513775%29
Again, the answer is: 4.46410161513775, -2.46410161513775. 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-11+%29

4x%5E2%2B4x=5=
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B4x%2B-5+=+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=%284%29%5E2-4%2A4%2A-5=96.

Discriminant d=96 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+96+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+96+%29%29%2F2%5C4+=+0.724744871391589
x%5B2%5D+=+%28-%284%29-sqrt%28+96+%29%29%2F2%5C4+=+-1.72474487139159

Quadratic expression 4x%5E2%2B4x%2B-5 can be factored:
4x%5E2%2B4x%2B-5+=+%28x-0.724744871391589%29%2A%28x--1.72474487139159%29
Again, the answer is: 0.724744871391589, -1.72474487139159. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B4%2Ax%2B-5+%29