x^2+x=14

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Solution for x^2+x=14 equation:


Simplifying
x2 + x = 14

Reorder the terms:
x + x2 = 14

Solving
x + x2 = 14

Solving for variable 'x'.

Reorder the terms:
-14 + x + x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + x + x2 = 0 + 14
x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
x + x2 = 14

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 = 14 + 0.25

Reorder the terms:
0.25 + x + x2 = 14 + 0.25

Combine like terms: 14 + 0.25 = 14.25
0.25 + x + x2 = 14.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.774917218 and -3.774917218.

Subproblem 1

x + 0.5 = 3.774917218 Simplifying x + 0.5 = 3.774917218 Reorder the terms: 0.5 + x = 3.774917218 Solving 0.5 + x = 3.774917218 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 = 3.774917218 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.774917218 + -0.5 x = 3.774917218 + -0.5 Combine like terms: 3.774917218 + -0.5 = 3.274917218 x = 3.274917218 Simplifying x = 3.274917218

Subproblem 2

x + 0.5 = -3.774917218 Simplifying x + 0.5 = -3.774917218 Reorder the terms: 0.5 + x = -3.774917218 Solving 0.5 + x = -3.774917218 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 = -3.774917218 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.774917218 + -0.5 x = -3.774917218 + -0.5 Combine like terms: -3.774917218 + -0.5 = -4.274917218 x = -4.274917218 Simplifying x = -4.274917218

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.274917218, -4.274917218}

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