SOLUTION: Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. 2a^2-46a+252=0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. 2a^2-46a+252=0      Log On


   

Question 195677: Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
2a^2-46a+252=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2a%5E2-46a%2B252=0 Start with the given equation.


Notice we have a quadratic equation in the form of Aa%5E2%2BBa%2BC=0 where A=2, B=-46, and C=252


Let's use the quadratic formula to solve for "a"


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


a+=+%28-%28-46%29+%2B-+sqrt%28+%28-46%29%5E2-4%282%29%28252%29+%29%29%2F%282%282%29%29 Plug in A=2, B=-46, and C=252


a+=+%2846+%2B-+sqrt%28+%28-46%29%5E2-4%282%29%28252%29+%29%29%2F%282%282%29%29 Negate -46 to get 46.


a+=+%2846+%2B-+sqrt%28+2116-4%282%29%28252%29+%29%29%2F%282%282%29%29 Square -46 to get 2116.


a+=+%2846+%2B-+sqrt%28+2116-2016+%29%29%2F%282%282%29%29 Multiply 4%282%29%28252%29 to get 2016


a+=+%2846+%2B-+sqrt%28+100+%29%29%2F%282%282%29%29 Subtract 2016 from 2116 to get 100


a+=+%2846+%2B-+sqrt%28+100+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


a+=+%2846+%2B-+10%29%2F%284%29 Take the square root of 100 to get 10.


a+=+%2846+%2B+10%29%2F%284%29 or a+=+%2846+-+10%29%2F%284%29 Break up the expression.


a+=+%2856%29%2F%284%29 or a+=++%2836%29%2F%284%29 Combine like terms.


a+=+14 or a+=+9 Simplify.


So the solutions are a+=+14 or a+=+9