x^2+x-5=150

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Solution for x^2+x-5=150 equation:


Simplifying
x2 + x + -5 = 150

Reorder the terms:
-5 + x + x2 = 150

Solving
-5 + x + x2 = 150

Solving for variable 'x'.

Reorder the terms:
-5 + -150 + x + x2 = 150 + -150

Combine like terms: -5 + -150 = -155
-155 + x + x2 = 150 + -150

Combine like terms: 150 + -150 = 0
-155 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '155' to each side of the equation.
-155 + x + 155 + x2 = 0 + 155

Reorder the terms:
-155 + 155 + x + x2 = 0 + 155

Combine like terms: -155 + 155 = 0
0 + x + x2 = 0 + 155
x + x2 = 0 + 155

Combine like terms: 0 + 155 = 155
x + x2 = 155

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 = 155 + 0.25

Reorder the terms:
0.25 + x + x2 = 155 + 0.25

Combine like terms: 155 + 0.25 = 155.25
0.25 + x + x2 = 155.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 155.25

Calculate the square root of the right side: 12.459935794

Break this problem into two subproblems by setting 
(x + 0.5) equal to 12.459935794 and -12.459935794.

Subproblem 1

x + 0.5 = 12.459935794 Simplifying x + 0.5 = 12.459935794 Reorder the terms: 0.5 + x = 12.459935794 Solving 0.5 + x = 12.459935794 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 = 12.459935794 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 12.459935794 + -0.5 x = 12.459935794 + -0.5 Combine like terms: 12.459935794 + -0.5 = 11.959935794 x = 11.959935794 Simplifying x = 11.959935794

Subproblem 2

x + 0.5 = -12.459935794 Simplifying x + 0.5 = -12.459935794 Reorder the terms: 0.5 + x = -12.459935794 Solving 0.5 + x = -12.459935794 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 = -12.459935794 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -12.459935794 + -0.5 x = -12.459935794 + -0.5 Combine like terms: -12.459935794 + -0.5 = -12.959935794 x = -12.959935794 Simplifying x = -12.959935794

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.959935794, -12.959935794}

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