10x^2-5x+11=-x^2+x+83

Simple and best practice solution for 10x^2-5x+11=-x^2+x+83 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 10x^2-5x+11=-x^2+x+83 equation:


Simplifying
10x2 + -5x + 11 = -1x2 + x + 83

Reorder the terms:
11 + -5x + 10x2 = -1x2 + x + 83

Reorder the terms:
11 + -5x + 10x2 = 83 + x + -1x2

Solving
11 + -5x + 10x2 = 83 + x + -1x2

Solving for variable 'x'.

Reorder the terms:
11 + -83 + -5x + -1x + 10x2 + x2 = 83 + x + -1x2 + -83 + -1x + x2

Combine like terms: 11 + -83 = -72
-72 + -5x + -1x + 10x2 + x2 = 83 + x + -1x2 + -83 + -1x + x2

Combine like terms: -5x + -1x = -6x
-72 + -6x + 10x2 + x2 = 83 + x + -1x2 + -83 + -1x + x2

Combine like terms: 10x2 + x2 = 11x2
-72 + -6x + 11x2 = 83 + x + -1x2 + -83 + -1x + x2

Reorder the terms:
-72 + -6x + 11x2 = 83 + -83 + x + -1x + -1x2 + x2

Combine like terms: 83 + -83 = 0
-72 + -6x + 11x2 = 0 + x + -1x + -1x2 + x2
-72 + -6x + 11x2 = x + -1x + -1x2 + x2

Combine like terms: x + -1x = 0
-72 + -6x + 11x2 = 0 + -1x2 + x2
-72 + -6x + 11x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-72 + -6x + 11x2 = 0

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

Divide each side by '11'.
-6.545454545 + -0.5454545455x + x2 = 0

Move the constant term to the right:

Add '6.545454545' to each side of the equation.
-6.545454545 + -0.5454545455x + 6.545454545 + x2 = 0 + 6.545454545

Reorder the terms:
-6.545454545 + 6.545454545 + -0.5454545455x + x2 = 0 + 6.545454545

Combine like terms: -6.545454545 + 6.545454545 = 0.000000000
0.000000000 + -0.5454545455x + x2 = 0 + 6.545454545
-0.5454545455x + x2 = 0 + 6.545454545

Combine like terms: 0 + 6.545454545 = 6.545454545
-0.5454545455x + x2 = 6.545454545

The x term is -0.5454545455x.  Take half its coefficient (-0.2727272728).
Square it (0.07438016533) and add it to both sides.

Add '0.07438016533' to each side of the equation.
-0.5454545455x + 0.07438016533 + x2 = 6.545454545 + 0.07438016533

Reorder the terms:
0.07438016533 + -0.5454545455x + x2 = 6.545454545 + 0.07438016533

Combine like terms: 6.545454545 + 0.07438016533 = 6.61983471033
0.07438016533 + -0.5454545455x + x2 = 6.61983471033

Factor a perfect square on the left side:
(x + -0.2727272728)(x + -0.2727272728) = 6.61983471033

Calculate the square root of the right side: 2.572903945

Break this problem into two subproblems by setting 
(x + -0.2727272728) equal to 2.572903945 and -2.572903945.

Subproblem 1

x + -0.2727272728 = 2.572903945 Simplifying x + -0.2727272728 = 2.572903945 Reorder the terms: -0.2727272728 + x = 2.572903945 Solving -0.2727272728 + x = 2.572903945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + x = 2.572903945 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + x = 2.572903945 + 0.2727272728 x = 2.572903945 + 0.2727272728 Combine like terms: 2.572903945 + 0.2727272728 = 2.8456312178 x = 2.8456312178 Simplifying x = 2.8456312178

Subproblem 2

x + -0.2727272728 = -2.572903945 Simplifying x + -0.2727272728 = -2.572903945 Reorder the terms: -0.2727272728 + x = -2.572903945 Solving -0.2727272728 + x = -2.572903945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + x = -2.572903945 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + x = -2.572903945 + 0.2727272728 x = -2.572903945 + 0.2727272728 Combine like terms: -2.572903945 + 0.2727272728 = -2.3001766722 x = -2.3001766722 Simplifying x = -2.3001766722

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.8456312178, -2.3001766722}

See similar equations:

| 198=-4x+2(-6x+15) | | M+80=0 | | (-28+8n)-5=-89 | | 3T+8=2T | | 3(2-2)+6=5(2+4) | | 3-5x=43 | | x^2+y^2+10y+18=0 | | b-2/3=-5/6 | | 1.2=4t | | 4+2n-1=8n+10-5n | | 5k-12=133 | | 3w/8=48 | | 10=-2+-2 | | 9(wx-v)=5(x+v) | | 5(c-16)=-5 | | 3/8u=42 | | 87=-4+7(7a-8) | | 0.4y+0.8(4)=0.5y(y+4) | | 5d+6=51 | | 0.7/3.5=0.2 | | 8m-3=5+7m-2m | | 8m+2=-33-39m | | 17.5/3.5=0.2 | | 5x-14=x^3 | | -2A+4B+C=0 | | 5x-14=3+x | | 8+30=70 | | 2(4y+3)+5y=-7 | | -8(x+-5)=22(x+-5)+540 | | 5d=9d-19 | | 423=9(x)+5(Y) | | X^2-2x-3=10 |

Equations solver categories