x^2+21x-40=0

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Solution for x^2+21x-40=0 equation: 


Simplifying
x2 + 21x + -40 = 0

Reorder the terms:
-40 + 21x + x2 = 0

Solving
-40 + 21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 21x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 21x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 21x + x2 = 0 + 40
21x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
21x + x2 = 40

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = 40 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 40 + 110.25

Combine like terms: 40 + 110.25 = 150.25
110.25 + 21x + x2 = 150.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 150.25

Calculate the square root of the right side: 12.257650672

Break this problem into two subproblems by setting 
(x + 10.5) equal to 12.257650672 and -12.257650672.


Subproblem 1
x + 10.5 = 12.257650672

Simplifying
x + 10.5 = 12.257650672

Reorder the terms:
10.5 + x = 12.257650672

Solving
10.5 + x = 12.257650672

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 12.257650672 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 12.257650672 + -10.5
x = 12.257650672 + -10.5

Combine like terms: 12.257650672 + -10.5 = 1.757650672
x = 1.757650672

Simplifying
x = 1.757650672


Subproblem 2
x + 10.5 = -12.257650672

Simplifying
x + 10.5 = -12.257650672

Reorder the terms:
10.5 + x = -12.257650672

Solving
10.5 + x = -12.257650672

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -12.257650672 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -12.257650672 + -10.5
x = -12.257650672 + -10.5

Combine like terms: -12.257650672 + -10.5 = -22.757650672
x = -22.757650672

Simplifying
x = -22.757650672


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.757650672, -22.757650672}

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