SOLUTION: Please help me solve this equation: 14=16t^2+12t

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Question 226662: Please help me solve this equation: 14=16t^2+12t
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve this equation: 14=16t%5E2%2B12t

Step 1. Subtract 14 from both sides of the equation.

14-14=16t%5E2%2B12t-14

0=16t%5E2%2B12t-14

Step 2. To solve, use the quadratic equation given as

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

where a=16, b=12, and c=-14

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 16x%5E2%2B12x%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=%2812%29%5E2-4%2A16%2A-14=1040.

Discriminant d=1040 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+1040+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+1040+%29%29%2F2%5C16+=+0.632782218537319
x%5B2%5D+=+%28-%2812%29-sqrt%28+1040+%29%29%2F2%5C16+=+-1.38278221853732

Quadratic expression 16x%5E2%2B12x%2B-14 can be factored:
16x%5E2%2B12x%2B-14+=+16%28x-0.632782218537319%29%2A%28x--1.38278221853732%29
Again, the answer is: 0.632782218537319, -1.38278221853732. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B12%2Ax%2B-14+%29



I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV