SOLUTION: How do you figure out this problem: -5x(2x-1)=3(x+4)

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Question 211912: How do you figure out this problem: -5x(2x-1)=3(x+4)
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
How do you figure out this problem: -5x(2x-1)=3(x+4)

Step 1. Multiply everything out on both sides of the equation. After we mess around with the equation, we will get a quadratic equation. Here it goes:

-5x(2x-1)=3(x+4) will yield: -10x^2+5x=3x+12.

Step 2. Now let's put everything on the right side so that the left side is zero. I like a positive number for the x^2 term.

Step 2a. Add 10x^2 to both sides of equation in Step 1:

10x^2-10x^2+5x=10x^2+3x+12

Note: The 10x^2 terms cancel out on the left side.

Step 2b. Simplify equation in step 2a.

5x=10x^2+3x+12

Step 3. Subtract 5x both sides of equation in Step 2b to make left side =0.

5x-5x=10x^2+3x-12-5x

Note: Collect like terms and simplify 3x-5x=-2x

Step 3a. Simplify to yield our final equation

0=10x^2-2x-12 OR 10x^2-2x-12=0

Step 4. Now we have a quadratic equation in step 3a.

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=10, b=-2, and c=-12.


Step 5. Substitute a, b, and c in the formula. The steps are shown below:

Note when the quadratic equation is a parabola when the values of x are real numbers. See graph where it intersects the x-axis. This is when y=0, hence our quadratic equation.

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 10x%5E2%2B-2x%2B-12+=+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%2A10%2A-12=484.

Discriminant d=484 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+484+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+484+%29%29%2F2%5C10+=+1.2
x%5B2%5D+=+%28-%28-2%29-sqrt%28+484+%29%29%2F2%5C10+=+-1

Quadratic expression 10x%5E2%2B-2x%2B-12 can be factored:
10x%5E2%2B-2x%2B-12+=+10%28x-1.2%29%2A%28x--1%29
Again, the answer is: 1.2, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+10%2Ax%5E2%2B-2%2Ax%2B-12+%29



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