5x^2+400x-2550=40

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Solution for 5x^2+400x-2550=40 equation: 


Simplifying
5x2 + 400x + -2550 = 40

Reorder the terms:
-2550 + 400x + 5x2 = 40

Solving
-2550 + 400x + 5x2 = 40

Solving for variable 'x'.

Reorder the terms:
-2550 + -40 + 400x + 5x2 = 40 + -40

Combine like terms: -2550 + -40 = -2590
-2590 + 400x + 5x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-2590 + 400x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-518 + 80x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-518 + 80x + x2)' equal to zero and attempt to solve:

Simplifying
-518 + 80x + x2 = 0

Solving
-518 + 80x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '518' to each side of the equation.
-518 + 80x + 518 + x2 = 0 + 518

Reorder the terms:
-518 + 518 + 80x + x2 = 0 + 518

Combine like terms: -518 + 518 = 0
0 + 80x + x2 = 0 + 518
80x + x2 = 0 + 518

Combine like terms: 0 + 518 = 518
80x + x2 = 518

The x term is 80x.  Take half its coefficient (40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
80x + 1600 + x2 = 518 + 1600

Reorder the terms:
1600 + 80x + x2 = 518 + 1600

Combine like terms: 518 + 1600 = 2118
1600 + 80x + x2 = 2118

Factor a perfect square on the left side:
(x + 40)(x + 40) = 2118

Calculate the square root of the right side: 46.021733996

Break this problem into two subproblems by setting 
(x + 40) equal to 46.021733996 and -46.021733996.


Subproblem 1
x + 40 = 46.021733996

Simplifying
x + 40 = 46.021733996

Reorder the terms:
40 + x = 46.021733996

Solving
40 + x = 46.021733996

Solving for variable 'x'.

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

Add '-40' to each side of the equation.
40 + -40 + x = 46.021733996 + -40

Combine like terms: 40 + -40 = 0
0 + x = 46.021733996 + -40
x = 46.021733996 + -40

Combine like terms: 46.021733996 + -40 = 6.021733996
x = 6.021733996

Simplifying
x = 6.021733996


Subproblem 2
x + 40 = -46.021733996

Simplifying
x + 40 = -46.021733996

Reorder the terms:
40 + x = -46.021733996

Solving
40 + x = -46.021733996

Solving for variable 'x'.

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

Add '-40' to each side of the equation.
40 + -40 + x = -46.021733996 + -40

Combine like terms: 40 + -40 = 0
0 + x = -46.021733996 + -40
x = -46.021733996 + -40

Combine like terms: -46.021733996 + -40 = -86.021733996
x = -86.021733996

Simplifying
x = -86.021733996


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.021733996, -86.021733996}
Solution
x = {6.021733996, -86.021733996}

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