x^2+x+0.5x=100

Simple and best practice solution for x^2+x+0.5x=100 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 x^2+x+0.5x=100 equation:


Simplifying
x2 + x + 0.5x = 100

Reorder the terms:
x + 0.5x + x2 = 100

Combine like terms: x + 0.5x = 1.5x
1.5x + x2 = 100

Solving
1.5x + x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + 1.5x + x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 1.5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 1.5x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + 1.5x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 1.5x + x2 = 0 + 100
1.5x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
1.5x + x2 = 100

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 100 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 100 + 0.5625

Combine like terms: 100 + 0.5625 = 100.5625
0.5625 + 1.5x + x2 = 100.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 100.5625

Calculate the square root of the right side: 10.02808556

Break this problem into two subproblems by setting 
(x + 0.75) equal to 10.02808556 and -10.02808556.

Subproblem 1

x + 0.75 = 10.02808556 Simplifying x + 0.75 = 10.02808556 Reorder the terms: 0.75 + x = 10.02808556 Solving 0.75 + x = 10.02808556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 10.02808556 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 10.02808556 + -0.75 x = 10.02808556 + -0.75 Combine like terms: 10.02808556 + -0.75 = 9.27808556 x = 9.27808556 Simplifying x = 9.27808556

Subproblem 2

x + 0.75 = -10.02808556 Simplifying x + 0.75 = -10.02808556 Reorder the terms: 0.75 + x = -10.02808556 Solving 0.75 + x = -10.02808556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -10.02808556 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -10.02808556 + -0.75 x = -10.02808556 + -0.75 Combine like terms: -10.02808556 + -0.75 = -10.77808556 x = -10.77808556 Simplifying x = -10.77808556

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.27808556, -10.77808556}

See similar equations:

| 46-2x=7x+24 | | 95+95+10x-5+8x+13=360 | | (x-1)/(x-7)=(2/5) | | x=1+-1.5y | | 3x-1=3(x+1) | | 2/3n-5/2 | | x+3/2=10 | | 4x^2-23x+23=-2x+3 | | x=10*3/2 | | 4x-10+2x+4=360 | | 8x+11+10x+105+82=360 | | 25.12=2r+3.14 | | 1/4(x+2)=4x-9(2-x)-7 | | a-(b+c-x)= | | .2x-2=3x+5.2 | | 9(t-5)+5t=7(2t+5)-10 | | 5k/6-k/4=-2 | | 80*37/40*1/4 | | 4x^2+20+9=0 | | ((-3x)/4)=(-1/2)-((x+3)/4) | | 5/11*77=35 | | (n-4)*4=28 | | 4(-7k+6)=136 | | x^2+17=-3x | | 2p^9q^6/r^8 | | 15-1/10x=1/5x | | n+32=19 | | 12x-24=9x+12 | | 6(x+3)=5x+6 | | x-7.7=-6.1 | | 18-(x+8)=5x-2 | | 2x^2-4x-12=0 |

Equations solver categories