x+102=x^2

Simple and best practice solution for x+102=x^2 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+102=x^2 equation:


Simplifying
x + 102 = x2

Reorder the terms:
102 + x = x2

Solving
102 + x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
102 + x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-102 + -1x + x2 = 0

Move the constant term to the right:

Add '102' to each side of the equation.
-102 + -1x + 102 + x2 = 0 + 102

Reorder the terms:
-102 + 102 + -1x + x2 = 0 + 102

Combine like terms: -102 + 102 = 0
0 + -1x + x2 = 0 + 102
-1x + x2 = 0 + 102

Combine like terms: 0 + 102 = 102
-1x + x2 = 102

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.
-1x + 0.25 + x2 = 102 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 102 + 0.25

Combine like terms: 102 + 0.25 = 102.25
0.25 + -1x + x2 = 102.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 102.25

Calculate the square root of the right side: 10.111874208

Break this problem into two subproblems by setting 
(x + 0.5) equal to 10.111874208 and -10.111874208.

Subproblem 1

x + 0.5 = 10.111874208 Simplifying x + 0.5 = 10.111874208 Reorder the terms: 0.5 + x = 10.111874208 Solving 0.5 + x = 10.111874208 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 = 10.111874208 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 10.111874208 + -0.5 x = 10.111874208 + -0.5 Combine like terms: 10.111874208 + -0.5 = 9.611874208 x = 9.611874208 Simplifying x = 9.611874208

Subproblem 2

x + 0.5 = -10.111874208 Simplifying x + 0.5 = -10.111874208 Reorder the terms: 0.5 + x = -10.111874208 Solving 0.5 + x = -10.111874208 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 = -10.111874208 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -10.111874208 + -0.5 x = -10.111874208 + -0.5 Combine like terms: -10.111874208 + -0.5 = -10.611874208 x = -10.611874208 Simplifying x = -10.611874208

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.611874208, -10.611874208}

See similar equations:

| 5(X+2)-4(X+1)=6 | | 2(5t-6)=15t+7 | | x-0.18x=112.30 | | cos(x)+2=0 | | 19-9=5x-3x | | 2x+4-3X=8(x-1) | | -11-1=4a-a | | 1/5x17 | | 5+2=2x-5x | | 4[6-(1-2x)+10]=2(10-3x) | | 2x^3-10x^2+8x=40 | | 7x-5x=-2-16 | | 7x-5x=-6-16 | | 6x+4-8x=9+3x | | 4w=1 | | -2w=-4 | | 14+3y=-2(9) | | -5w=-8 | | 5x+8=34 | | 1+9=7w-2w | | 1/3x^2-2x-7 | | 1+9=7x-2w | | 4.4x+49.4=20.2-10.2x | | 30+9x=12 | | 8x=-1.2 | | q(t)=(6t^2)+10t-10 | | x/4=50 | | 8x^2-11x-6=0 | | 7x+4=-80 | | 0x+4y=3 | | 4c+6c= | | 9x^2-139x+930=0 |

Equations solver categories