0.5x^2+x-500=0

Simple and best practice solution for 0.5x^2+x-500=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 0.5x^2+x-500=0 equation:


Simplifying
0.5x2 + x + -500 = 0

Reorder the terms:
-500 + x + 0.5x2 = 0

Solving
-500 + x + 0.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.5 the coefficient of the squared term: 

Divide each side by '0.5'.
-1000 + 2x + x2 = 0

Move the constant term to the right:

Add '1000' to each side of the equation.
-1000 + 2x + 1000 + x2 = 0 + 1000

Reorder the terms:
-1000 + 1000 + 2x + x2 = 0 + 1000

Combine like terms: -1000 + 1000 = 0
0 + 2x + x2 = 0 + 1000
2x + x2 = 0 + 1000

Combine like terms: 0 + 1000 = 1000
2x + x2 = 1000

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
2x + 0.25 + x2 = 1000 + 0.25

Reorder the terms:
0.25 + 2x + x2 = 1000 + 0.25

Combine like terms: 1000 + 0.25 = 1000.25
0.25 + 2x + x2 = 1000.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1000.25

Calculate the square root of the right side: 31.626729202

Break this problem into two subproblems by setting 
(x + 0.5) equal to 31.626729202 and -31.626729202.

Subproblem 1

x + 0.5 = 31.626729202 Simplifying x + 0.5 = 31.626729202 Reorder the terms: 0.5 + x = 31.626729202 Solving 0.5 + x = 31.626729202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 31.626729202 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 31.626729202 + -0.5 x = 31.626729202 + -0.5 Combine like terms: 31.626729202 + -0.5 = 31.126729202 x = 31.126729202 Simplifying x = 31.126729202

Subproblem 2

x + 0.5 = -31.626729202 Simplifying x + 0.5 = -31.626729202 Reorder the terms: 0.5 + x = -31.626729202 Solving 0.5 + x = -31.626729202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -31.626729202 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -31.626729202 + -0.5 x = -31.626729202 + -0.5 Combine like terms: -31.626729202 + -0.5 = -32.126729202 x = -32.126729202 Simplifying x = -32.126729202

Solution

The solution to the problem is based on the solutions from the subproblems. x = {31.126729202, -32.126729202}

See similar equations:

| 2x-1.4=0.6 | | (4x+32)+84=180 | | 8.4=x/100 | | 26=5(w+7)-8w | | -18=9n-17 | | x^2+10x-18=180 | | 2x^2-xy-6y^2+4x+6y=0 | | 18=3y-12fory | | 3/1-x/2 | | x-5x+8x-7x= | | -1.1p-3=1.6 | | -(3x-15)+2(6x+4)= | | 6(u-4)-2=-6(-3u+4)-6u | | 2p+21=5p+3 | | X+615=850 | | 3.99r=50+1.99r | | 1g-2/3g=-5/6 | | 1.2+3j=1.5 | | -4(w-5)=-7w+29 | | -(4x-10)+3(5x+7)= | | -8=3(u-4)-7u | | -8=3v+4 | | X+90=72 | | 212=76-x | | 7x-4=20x+3 | | 4b+2+52+74=180 | | 3y-17=22 | | 100x*2= | | 10x+25y=400 | | 180=4x-3+3x-1+x | | 3r=63.9 | | 4x-(3/4)=1/2 |

Equations solver categories