x^2+x=101

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Solution for x^2+x=101 equation:


Simplifying
x2 + x = 101

Reorder the terms:
x + x2 = 101

Solving
x + x2 = 101

Solving for variable 'x'.

Reorder the terms:
-101 + x + x2 = 101 + -101

Combine like terms: 101 + -101 = 0
-101 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '101' to each side of the equation.
-101 + x + 101 + x2 = 0 + 101

Reorder the terms:
-101 + 101 + x + x2 = 0 + 101

Combine like terms: -101 + 101 = 0
0 + x + x2 = 0 + 101
x + x2 = 0 + 101

Combine like terms: 0 + 101 = 101
x + x2 = 101

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.
x + 0.25 + x2 = 101 + 0.25

Reorder the terms:
0.25 + x + x2 = 101 + 0.25

Combine like terms: 101 + 0.25 = 101.25
0.25 + x + x2 = 101.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 101.25

Calculate the square root of the right side: 10.062305899

Break this problem into two subproblems by setting 
(x + 0.5) equal to 10.062305899 and -10.062305899.

Subproblem 1

x + 0.5 = 10.062305899 Simplifying x + 0.5 = 10.062305899 Reorder the terms: 0.5 + x = 10.062305899 Solving 0.5 + x = 10.062305899 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 = 10.062305899 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 10.062305899 + -0.5 x = 10.062305899 + -0.5 Combine like terms: 10.062305899 + -0.5 = 9.562305899 x = 9.562305899 Simplifying x = 9.562305899

Subproblem 2

x + 0.5 = -10.062305899 Simplifying x + 0.5 = -10.062305899 Reorder the terms: 0.5 + x = -10.062305899 Solving 0.5 + x = -10.062305899 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 = -10.062305899 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -10.062305899 + -0.5 x = -10.062305899 + -0.5 Combine like terms: -10.062305899 + -0.5 = -10.562305899 x = -10.562305899 Simplifying x = -10.562305899

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.562305899, -10.562305899}

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