x^2+x-20=24

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Solution for x^2+x-20=24 equation: 


Simplifying
x2 + x + -20 = 24

Reorder the terms:
-20 + x + x2 = 24

Solving
-20 + x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
-20 + -24 + x + x2 = 24 + -24

Combine like terms: -20 + -24 = -44
-44 + x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-44 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + x + 44 + x2 = 0 + 44

Reorder the terms:
-44 + 44 + x + x2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + x + x2 = 0 + 44
x + x2 = 0 + 44

Combine like terms: 0 + 44 = 44
x + x2 = 44

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 = 44 + 0.25

Reorder the terms:
0.25 + x + x2 = 44 + 0.25

Combine like terms: 44 + 0.25 = 44.25
0.25 + x + x2 = 44.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 44.25

Calculate the square root of the right side: 6.652067348

Break this problem into two subproblems by setting 
(x + 0.5) equal to 6.652067348 and -6.652067348.


Subproblem 1
x + 0.5 = 6.652067348

Simplifying
x + 0.5 = 6.652067348

Reorder the terms:
0.5 + x = 6.652067348

Solving
0.5 + x = 6.652067348

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 = 6.652067348 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 6.652067348 + -0.5
x = 6.652067348 + -0.5

Combine like terms: 6.652067348 + -0.5 = 6.152067348
x = 6.152067348

Simplifying
x = 6.152067348


Subproblem 2
x + 0.5 = -6.652067348

Simplifying
x + 0.5 = -6.652067348

Reorder the terms:
0.5 + x = -6.652067348

Solving
0.5 + x = -6.652067348

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 = -6.652067348 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -6.652067348 + -0.5
x = -6.652067348 + -0.5

Combine like terms: -6.652067348 + -0.5 = -7.152067348
x = -7.152067348

Simplifying
x = -7.152067348


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.152067348, -7.152067348}

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