SOLUTION: solve the following quadratic equation. round answers 2 decimal places. 0.7x^2= 0.1x+0.3

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: solve the following quadratic equation. round answers 2 decimal places. 0.7x^2= 0.1x+0.3      Log On


   

Question 212952: solve the following quadratic equation. round answers 2 decimal places.
0.7x^2= 0.1x+0.3
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following quadratic equation. round answers 2 decimal places.

0.7x%5E2=+0.1x%2B0.3

Let's put the above equation in quadratic form by subtracting 0.1x+.3 from both sides of the equation


0.7x%5E2-%280.1x%2B0.3%29=+0.1x%2B0.3-%280.1x%2B0.3%29

0.7x%5E2-0.1x-0.3+=+0

Multiply by ten to get rid of decimal point

7x%5E2-1x-3+=+0

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 7x%5E2%2B-1x%2B-3+=+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%2A7%2A-3=85.

Discriminant d=85 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+85+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+85+%29%29%2F2%5C7+=+0.729967461235206
x%5B2%5D+=+%28-%28-1%29-sqrt%28+85+%29%29%2F2%5C7+=+-0.587110318378063

Quadratic expression 7x%5E2%2B-1x%2B-3 can be factored:
7x%5E2%2B-1x%2B-3+=+7%28x-0.729967461235206%29%2A%28x--0.587110318378063%29
Again, the answer is: 0.729967461235206, -0.587110318378063. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+7%2Ax%5E2%2B-1%2Ax%2B-3+%29



I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J