SOLUTION: Solve using the quadratic formula {{{3x^2-14x=-15}}} {{{5x^2=x+2}}} {{{4x^2=12x-9}}} I need help on these also it looks like this on the paper Solve. Express irrationa

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve using the quadratic formula {{{3x^2-14x=-15}}} {{{5x^2=x+2}}} {{{4x^2=12x-9}}} I need help on these also it looks like this on the paper Solve. Express irrationa      Log On


   

Question 38943: Solve using the quadratic formula
3x%5E2-14x=-15
5x%5E2=x%2B2
4x%5E2=12x-9
I need help on these also it looks like this on the paper
Solve. Express irrational solutions in simplest radical form.
2x%5E2=128
x%5E2%2B25=0
x%5E2=25%2F36
0=6x%5E2-24
2%28x%2B3%29%5E2-4=68
x%5E2%2B5x-24=0
x%5E2-3x-28=0
x%5E2-49=0
5x%5E2-2x-7=0
+sqrt+%283x=9%29+
+sqrt+%28x%2B2-7=2%29+
+sqrt+%28x-4-9=4%29+

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2-14x%2B15=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-14x%2B15+=+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=%28-14%29%5E2-4%2A3%2A15=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--14%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-14%29%2Bsqrt%28+16+%29%29%2F2%5C3+=+3
x%5B2%5D+=+%28-%28-14%29-sqrt%28+16+%29%29%2F2%5C3+=+1.66666666666667

Quadratic expression 3x%5E2%2B-14x%2B15 can be factored:
3x%5E2%2B-14x%2B15+=+3%28x-3%29%2A%28x-1.66666666666667%29
Again, the answer is: 3, 1.66666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-14%2Ax%2B15+%29

.
5x%5E2-x-2=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-1x%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=%28-1%29%5E2-4%2A5%2A-2=41.

Discriminant d=41 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+41+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+41+%29%29%2F2%5C5+=+0.740312423743285
x%5B2%5D+=+%28-%28-1%29-sqrt%28+41+%29%29%2F2%5C5+=+-0.540312423743285

Quadratic expression 5x%5E2%2B-1x%2B-2 can be factored:
5x%5E2%2B-1x%2B-2+=+5%28x-0.740312423743285%29%2A%28x--0.540312423743285%29
Again, the answer is: 0.740312423743285, -0.540312423743285. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-1%2Ax%2B-2+%29

.
4x%5E2-12x%2B9=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-12x%2B9+=+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=%28-12%29%5E2-4%2A4%2A9=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%28-12%29%29%2F2%5C4.
Expression can be factored: 4x%5E2%2B-12x%2B9+=+4%28x-1.5%29%2A%28x-1.5%29

Again, the answer is: 1.5, 1.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-12%2Ax%2B9+%29

.
2x%5E2=128
x%5E2=64
x=8 or x=-8
.
x%5E2%2B25=0
x%5E2=-25
x=5i or -5i
.
x%5E2=25%2F36
x=5%2F6 or x=-5%2F6
.
0=6x%5E2-24
-6x%5E2=-24%7D%7D%0D%0A%7B%7B%7Bx%5E2=4
x=2 or x=-2
.
2%28x%2B3%29%5E2-4=68
2%28x%5E2%2B6x%2B9%29-4=68
2x%5E2%2B12x%2B18-4-68
2x%5E2%2B12x-54=0
x%5E2%2B6x-27=0
x%5E2%2B9x-3x-27=0
%28x%5E2%2B9x%29%2B%28-3x-27%29=0
x%28x%2B9%29-3%28x%2B9%29=0
%28x-3%29%28x%2B9%29=0
x=3 or x=-9
.
x%5E2%2B5x-24=0
x%5E2%2B8x-3x-24=0
%28x%5E2%2B8x%29%2B%28-3x-24%29=0
x%28x%2B8%29-3%28x%2B8%29=0
%28x-3%29%28x%2B8%29=0
x=3 or x=-8
.
x%5E2-3x-28=0
%28x%5E2-7x%29%2B%284x-28%29=0
x%28x-7%29%2B4%28x-7%29=0
%28x%2B4%29%28x-7%29=0
x=-4 or x=7
.
x%5E2-49=0
x%5E2=49
x=-7 or x=7
.
5x%5E2-2x-7=0
%285x%5E2-7x%29%2B%285x-7%29=0
x%285x-7%29%2B1%285x-7%29=0
%28x%2B1%29%285x-7%29=0
x=-1 or x=7%2F5
.
I do not know why the next problems are all under the square root sign, but i bet you can do those. Remember, no value that is negative should be under a square root sign when you are not dealing with complex solutions.