SOLUTION: Use any method to solve the equation. If necessary, round to the nearest hundredth. 8xˆ2 + 18x -24 = 0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Use any method to solve the equation. If necessary, round to the nearest hundredth. 8xˆ2 + 18x -24 = 0       Log On


   

Question 473387: Use any method to solve the equation. If necessary, round to the nearest hundredth.
8xˆ2 + 18x -24 = 0
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


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




So lets solve 8%2Ax%5E2%2B18%2Ax-24=0 ( notice a=8, b=18, and c=-24)





x+=+%28-18+%2B-+sqrt%28+%2818%29%5E2-4%2A8%2A-24+%29%29%2F%282%2A8%29 Plug in a=8, b=18, and c=-24




x+=+%28-18+%2B-+sqrt%28+324-4%2A8%2A-24+%29%29%2F%282%2A8%29 Square 18 to get 324




x+=+%28-18+%2B-+sqrt%28+324%2B768+%29%29%2F%282%2A8%29 Multiply -4%2A-24%2A8 to get 768




x+=+%28-18+%2B-+sqrt%28+1092+%29%29%2F%282%2A8%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-18+%2B-+2%2Asqrt%28273%29%29%2F%282%2A8%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-18+%2B-+2%2Asqrt%28273%29%29%2F16 Multiply 2 and 8 to get 16


So now the expression breaks down into two parts


x+=+%28-18+%2B+2%2Asqrt%28273%29%29%2F16 or x+=+%28-18+-+2%2Asqrt%28273%29%29%2F16



Now break up the fraction



x=-18%2F16%2B2%2Asqrt%28273%29%2F16 or x=-18%2F16-2%2Asqrt%28273%29%2F16



Simplify



x=-9%2F8%2Bsqrt%28273%29%2F8 or x=-9%2F8-sqrt%28273%29%2F8



So the solutions are:

x=-9%2F8%2Bsqrt%28273%29%2F8 or x=-9%2F8-sqrt%28273%29%2F8





x=-9%2F8%2B16.52%2F8 or x=-9%2F8-16.52%2F8
x=-1.125%2B2.065 or x=-1.125-2.065+
x=0.94 or x=-3.19+