2x^2+21x-40=0

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


Simplifying
2x2 + 21x + -40 = 0

Reorder the terms:
-40 + 21x + 2x2 = 0

Solving
-40 + 21x + 2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-20 + 10.5x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 10.5x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 10.5x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 10.5x + x2 = 0 + 20
10.5x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
10.5x + x2 = 20

The x term is 10.5x.  Take half its coefficient (5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
10.5x + 27.5625 + x2 = 20 + 27.5625

Reorder the terms:
27.5625 + 10.5x + x2 = 20 + 27.5625

Combine like terms: 20 + 27.5625 = 47.5625
27.5625 + 10.5x + x2 = 47.5625

Factor a perfect square on the left side:
(x + 5.25)(x + 5.25) = 47.5625

Calculate the square root of the right side: 6.896557112

Break this problem into two subproblems by setting 
(x + 5.25) equal to 6.896557112 and -6.896557112.


Subproblem 1
x + 5.25 = 6.896557112

Simplifying
x + 5.25 = 6.896557112

Reorder the terms:
5.25 + x = 6.896557112

Solving
5.25 + x = 6.896557112

Solving for variable 'x'.

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

Add '-5.25' to each side of the equation.
5.25 + -5.25 + x = 6.896557112 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + x = 6.896557112 + -5.25
x = 6.896557112 + -5.25

Combine like terms: 6.896557112 + -5.25 = 1.646557112
x = 1.646557112

Simplifying
x = 1.646557112


Subproblem 2
x + 5.25 = -6.896557112

Simplifying
x + 5.25 = -6.896557112

Reorder the terms:
5.25 + x = -6.896557112

Solving
5.25 + x = -6.896557112

Solving for variable 'x'.

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

Add '-5.25' to each side of the equation.
5.25 + -5.25 + x = -6.896557112 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + x = -6.896557112 + -5.25
x = -6.896557112 + -5.25

Combine like terms: -6.896557112 + -5.25 = -12.146557112
x = -12.146557112

Simplifying
x = -12.146557112


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.646557112, -12.146557112}

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