SOLUTION: Please disregard my previous problem I wrote it wrong. Use the Quadratic Formula to solve. 0.5x^2=x+0.5

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Please disregard my previous problem I wrote it wrong. Use the Quadratic Formula to solve. 0.5x^2=x+0.5      Log On


   

Question 290274: Please disregard my previous problem I wrote it wrong.
Use the Quadratic Formula to solve.
0.5x^2=x+0.5
Found 2 solutions by jim_thompson5910, Earlsdon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
0.5x%5E2=x%2B0.5 Start with the given equation.


x%5E2=2x%2B1 Multiply EVERY term by 2 (note: 0.5=1%2F2) to clear out the decimals.


x%5E2-2x-1=0 Get every term to the left side.


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 x%5E2-2%2Ax-1=0 ( notice a=1, b=-2, and c=-1)





x+=+%28--2+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A-1+%29%29%2F%282%2A1%29 Plug in a=1, b=-2, and c=-1




x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A-1+%29%29%2F%282%2A1%29 Negate -2 to get 2




x+=+%282+%2B-+sqrt%28+4-4%2A1%2A-1+%29%29%2F%282%2A1%29 Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because %28-2%29%5E2=-2%2A-2=4.)




x+=+%282+%2B-+sqrt%28+4%2B4+%29%29%2F%282%2A1%29 Multiply -4%2A-1%2A1 to get 4




x+=+%282+%2B-+sqrt%28+8+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%282+%2B-+2%2Asqrt%282%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%282+%2B-+2%2Asqrt%282%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%282+%2B+2%2Asqrt%282%29%29%2F2 or x+=+%282+-+2%2Asqrt%282%29%29%2F2



Now break up the fraction



x=%2B2%2F2%2B2%2Asqrt%282%29%2F2 or x=%2B2%2F2-2%2Asqrt%282%29%2F2



Simplify



x=1%2Bsqrt%282%29 or x=1-sqrt%282%29



So the solutions are:

x=1%2Bsqrt%282%29 or x=1-sqrt%282%29






So the solutions are x=1%2Bsqrt%282%29 or x=1-sqrt%282%29

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve, using the quadratic formula:x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
0.5x%5E2+=+x%2B0.5 Subtract (x+0.5) from both sides.
0.5x%5E2-x-0.5+=+0 a = 0.5, b = -1, and c = -0.5
x+=+%28-%28-1%29%2B-sqrt%28%28-1%29%5E2-4%280.5%29%28-0.5%29%29%29%2F2%280.5%29
x+=+%281%2B-sqrt%281-4%28-0.25%29%29%29%2F1
highlight%28x+=+1%2B-sqrt%282%29%29