SOLUTION: Hi everyone, I would like some help with the following question. I need to solve the following quadratic expression: x^2 - 5x - 14 = 0 If someone could show me how and explain

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hi everyone, I would like some help with the following question. I need to solve the following quadratic expression: x^2 - 5x - 14 = 0 If someone could show me how and explain      Log On


   

Question 200490: Hi everyone, I would like some help with the following question.
I need to solve the following quadratic expression:
x^2 - 5x - 14 = 0
If someone could show me how and explain with steps that would be great.
Thanks, -Nick.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-5x-14=0 Start with the given equation.


Notice that the quadratic x%5E2-5x-14 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-5, and C=-14


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%28-14%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-5, and C=-14


x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%28-14%29+%29%29%2F%282%281%29%29 Negate -5 to get 5.


x+=+%285+%2B-+sqrt%28+25-4%281%29%28-14%29+%29%29%2F%282%281%29%29 Square -5 to get 25.


x+=+%285+%2B-+sqrt%28+25--56+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-14%29 to get -56


x+=+%285+%2B-+sqrt%28+25%2B56+%29%29%2F%282%281%29%29 Rewrite sqrt%2825--56%29 as sqrt%2825%2B56%29


x+=+%285+%2B-+sqrt%28+81+%29%29%2F%282%281%29%29 Add 25 to 56 to get 81


x+=+%285+%2B-+sqrt%28+81+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%285+%2B-+9%29%2F%282%29 Take the square root of 81 to get 9.


x+=+%285+%2B+9%29%2F%282%29 or x+=+%285+-+9%29%2F%282%29 Break up the expression.


x+=+%2814%29%2F%282%29 or x+=++%28-4%29%2F%282%29 Combine like terms.


x+=+7 or x+=+-2 Simplify.


So the solutions are x+=+7 or x+=+-2