SOLUTION: Please help me with these three problems. Solve each equation by using the quadratic formula. Give exact and approximate answers to the nearest tenth. 1. 5x^-9x=3=0

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Question 37620: Please help me with these three problems.
Solve each equation by using the quadratic formula. Give exact and approximate answers to the nearest tenth.
1. 5x^-9x=3=0
2. x^=54-3x
Find the equation of the axis of symmetry, the coordinates of the vertex, and the coordinates of the x-intercepts, if they exist, for each parabola.
3. f(x) = 2x6-3x-14
Thank you very much
Answer by jessicaherndon(6) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-9x%2B3+=+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=%28-9%29%5E2-4%2A5%2A3=21.

Discriminant d=21 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--9%2B-sqrt%28+21+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+21+%29%29%2F2%5C5+=+1.35825756949558
x%5B2%5D+=+%28-%28-9%29-sqrt%28+21+%29%29%2F2%5C5+=+0.441742430504416

Quadratic expression 5x%5E2%2B-9x%2B3 can be factored:
5x%5E2%2B-9x%2B3+=+5%28x-1.35825756949558%29%2A%28x-0.441742430504416%29
Again, the answer is: 1.35825756949558, 0.441742430504416. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-9%2Ax%2B3+%29


Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-3x%2B-14+=+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=%28-3%29%5E2-4%2A2%2A-14=121.

Discriminant d=121 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+121+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+121+%29%29%2F2%5C2+=+3.5
x%5B2%5D+=+%28-%28-3%29-sqrt%28+121+%29%29%2F2%5C2+=+-2

Quadratic expression 2x%5E2%2B-3x%2B-14 can be factored:
2x%5E2%2B-3x%2B-14+=+2%28x-3.5%29%2A%28x--2%29
Again, the answer is: 3.5, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-3%2Ax%2B-14+%29