SOLUTION: Please show me the steps to doing this problem...I can't figure this one out Solve equation using the quadratic formula 4x^2 =2x + 1 Thank you very much

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please show me the steps to doing this problem...I can't figure this one out Solve equation using the quadratic formula 4x^2 =2x + 1 Thank you very much      Log On


   

Question 169892: Please show me the steps to doing this problem...I can't figure this one out
Solve equation using the quadratic formula
4x^2 =2x + 1
Thank you very much
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2=2x%2B1 Start with the given equation.


4x%5E2-2x-1=0 Get all terms to the left side.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=4, b=-2, and c=-1


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-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%284%29%28-1%29+%29%29%2F%282%284%29%29 Plug in a=4, b=-2, and c=-1


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%284%29%28-1%29+%29%29%2F%282%284%29%29 Negate -2 to get 2.


x+=+%282+%2B-+sqrt%28+4-4%284%29%28-1%29+%29%29%2F%282%284%29%29 Square -2 to get 4.


x+=+%282+%2B-+sqrt%28+4--16+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-1%29 to get -16


x+=+%282+%2B-+sqrt%28+4%2B16+%29%29%2F%282%284%29%29 Rewrite sqrt%284--16%29 as sqrt%284%2B16%29


x+=+%282+%2B-+sqrt%28+20+%29%29%2F%282%284%29%29 Add 4 to 16 to get 20


x+=+%282+%2B-+sqrt%28+20+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%282+%2B-+2%2Asqrt%285%29%29%2F%288%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%282%2B2%2Asqrt%285%29%29%2F%288%29 or x+=+%282-2%2Asqrt%285%29%29%2F%288%29 Break up the expression.


x+=+%281%2Bsqrt%285%29%29%2F%284%29 or x+=+%281-sqrt%285%29%29%2F%284%29 Reduce


So the answers are x+=+%281%2Bsqrt%285%29%29%2F%284%29 or x+=+%281-sqrt%285%29%29%2F%284%29


which approximate to x=0.809 or x=-0.309