x^2+x=10

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Solution for x^2+x=10 equation:


Simplifying
x2 + x = 10

Reorder the terms:
x + x2 = 10

Solving
x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + x + x2 = 0 + 10
x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
x + x2 = 10

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 = 10 + 0.25

Reorder the terms:
0.25 + x + x2 = 10 + 0.25

Combine like terms: 10 + 0.25 = 10.25
0.25 + x + x2 = 10.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.201562119 and -3.201562119.

Subproblem 1

x + 0.5 = 3.201562119 Simplifying x + 0.5 = 3.201562119 Reorder the terms: 0.5 + x = 3.201562119 Solving 0.5 + x = 3.201562119 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 = 3.201562119 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.201562119 + -0.5 x = 3.201562119 + -0.5 Combine like terms: 3.201562119 + -0.5 = 2.701562119 x = 2.701562119 Simplifying x = 2.701562119

Subproblem 2

x + 0.5 = -3.201562119 Simplifying x + 0.5 = -3.201562119 Reorder the terms: 0.5 + x = -3.201562119 Solving 0.5 + x = -3.201562119 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 = -3.201562119 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.201562119 + -0.5 x = -3.201562119 + -0.5 Combine like terms: -3.201562119 + -0.5 = -3.701562119 x = -3.701562119 Simplifying x = -3.701562119

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.701562119, -3.701562119}

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