400-80x-40+3x^2+4x=80

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Solution for 400-80x-40+3x^2+4x=80 equation:


Simplifying
400 + -80x + -40 + 3x2 + 4x = 80

Reorder the terms:
400 + -40 + -80x + 4x + 3x2 = 80

Combine like terms: 400 + -40 = 360
360 + -80x + 4x + 3x2 = 80

Combine like terms: -80x + 4x = -76x
360 + -76x + 3x2 = 80

Solving
360 + -76x + 3x2 = 80

Solving for variable 'x'.

Reorder the terms:
360 + -80 + -76x + 3x2 = 80 + -80

Combine like terms: 360 + -80 = 280
280 + -76x + 3x2 = 80 + -80

Combine like terms: 80 + -80 = 0
280 + -76x + 3x2 = 0

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

Divide each side by '3'.
93.33333333 + -25.33333333x + x2 = 0

Move the constant term to the right:

Add '-93.33333333' to each side of the equation.
93.33333333 + -25.33333333x + -93.33333333 + x2 = 0 + -93.33333333

Reorder the terms:
93.33333333 + -93.33333333 + -25.33333333x + x2 = 0 + -93.33333333

Combine like terms: 93.33333333 + -93.33333333 = 0.00000000
0.00000000 + -25.33333333x + x2 = 0 + -93.33333333
-25.33333333x + x2 = 0 + -93.33333333

Combine like terms: 0 + -93.33333333 = -93.33333333
-25.33333333x + x2 = -93.33333333

The x term is -25.33333333x.  Take half its coefficient (-12.66666667).
Square it (160.4444445) and add it to both sides.

Add '160.4444445' to each side of the equation.
-25.33333333x + 160.4444445 + x2 = -93.33333333 + 160.4444445

Reorder the terms:
160.4444445 + -25.33333333x + x2 = -93.33333333 + 160.4444445

Combine like terms: -93.33333333 + 160.4444445 = 67.11111117
160.4444445 + -25.33333333x + x2 = 67.11111117

Factor a perfect square on the left side:
(x + -12.66666667)(x + -12.66666667) = 67.11111117

Calculate the square root of the right side: 8.192137155

Break this problem into two subproblems by setting 
(x + -12.66666667) equal to 8.192137155 and -8.192137155.

Subproblem 1

x + -12.66666667 = 8.192137155 Simplifying x + -12.66666667 = 8.192137155 Reorder the terms: -12.66666667 + x = 8.192137155 Solving -12.66666667 + x = 8.192137155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.66666667' to each side of the equation. -12.66666667 + 12.66666667 + x = 8.192137155 + 12.66666667 Combine like terms: -12.66666667 + 12.66666667 = 0.00000000 0.00000000 + x = 8.192137155 + 12.66666667 x = 8.192137155 + 12.66666667 Combine like terms: 8.192137155 + 12.66666667 = 20.858803825 x = 20.858803825 Simplifying x = 20.858803825

Subproblem 2

x + -12.66666667 = -8.192137155 Simplifying x + -12.66666667 = -8.192137155 Reorder the terms: -12.66666667 + x = -8.192137155 Solving -12.66666667 + x = -8.192137155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.66666667' to each side of the equation. -12.66666667 + 12.66666667 + x = -8.192137155 + 12.66666667 Combine like terms: -12.66666667 + 12.66666667 = 0.00000000 0.00000000 + x = -8.192137155 + 12.66666667 x = -8.192137155 + 12.66666667 Combine like terms: -8.192137155 + 12.66666667 = 4.474529515 x = 4.474529515 Simplifying x = 4.474529515

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20.858803825, 4.474529515}

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