SOLUTION: (pretend exponets ^1) 1. What is the positive solution of 3x^2 -10x-8=0? 2. A triangular-shaped wall has a base of 2x +4 and a height of x +3. The area of the triangle is 56 i

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: (pretend exponets ^1) 1. What is the positive solution of 3x^2 -10x-8=0? 2. A triangular-shaped wall has a base of 2x +4 and a height of x +3. The area of the triangle is 56 i      Log On


   

Question 950051: (pretend exponets ^1)
1. What is the positive solution of 3x^2 -10x-8=0?
2. A triangular-shaped wall has a base of 2x +4 and a height of x +3. The area of the triangle is 56 in^.2.What is the value of x?
Found 2 solutions by Fombitz, macston:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2+-10x-8=0
%28x-4%29%283x%2B2%29=0
Only the positive solution,
x-4=0
x=4
.
.
.
The area of a triangle is,
A=%281%2F2%29bh=56
bh=112
%282x%2B4%29%28x%2B3%29=56
2x%5E2%2B6x%2B4x%2B12=56
2x%5E2%2B10x-44=0
x%5E2%2B5x-22=0
x%5E2%2B5x%2B%285%2F2%29%5E2-22=%285%2F2%29%5E2
%28x%2B5%2F2%29%5E2=%2825%2F4%29%2B22
%28x%2B5%2F2%29%5E2=%2825%2F4%29%2B88%2F4
%28x%2B5%2F2%29%5E2=113%2F4
x%2B5%2F2=0+%2B-+sqrt%28113%29%2F2
x=-5%2F2+%2B-+sqrt%28113%29%2F2
Only the positive solution works here,
x=%28sqrt%28113%29-5%29%2F2


Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
PROBLEM 1:
3x%5E2-10x-8=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-10x%2B-8+=+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=%28-10%29%5E2-4%2A3%2A-8=196.

Discriminant d=196 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+196+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+196+%29%29%2F2%5C3+=+4
x%5B2%5D+=+%28-%28-10%29-sqrt%28+196+%29%29%2F2%5C3+=+-0.666666666666667

Quadratic expression 3x%5E2%2B-10x%2B-8 can be factored:
3x%5E2%2B-10x%2B-8+=+3%28x-4%29%2A%28x--0.666666666666667%29
Again, the answer is: 4, -0.666666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-10%2Ax%2B-8+%29

ANSWER: The positive solution is 4.
PROBLEM 2:
b=base; h=height; a=area=1/2(b)(h)
a=%281%2F2%29bh
56+in%5E2=%281%2F2%29%282x%2B4%29%28x%2B3%29
56+in%5E2=%28x%2B2%29%28x%2B3%29
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B5x%2B-50+=+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=%285%29%5E2-4%2A1%2A-50=225.

Discriminant d=225 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+225+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+225+%29%29%2F2%5C1+=+5
x%5B2%5D+=+%28-%285%29-sqrt%28+225+%29%29%2F2%5C1+=+-10

Quadratic expression 1x%5E2%2B5x%2B-50 can be factored:
1x%5E2%2B5x%2B-50+=+1%28x-5%29%2A%28x--10%29
Again, the answer is: 5, -10. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-50+%29

Our answer is the positive solution. ANSWER: The value of x is 5.