(x^2)+40x+40=4x+4

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Solution for (x^2)+40x+40=4x+4 equation:


Simplifying
(x2) + 40x + 40 = 4x + 4
x2 + 40x + 40 = 4x + 4

Reorder the terms:
40 + 40x + x2 = 4x + 4

Reorder the terms:
40 + 40x + x2 = 4 + 4x

Solving
40 + 40x + x2 = 4 + 4x

Solving for variable 'x'.

Reorder the terms:
40 + -4 + 40x + -4x + x2 = 4 + 4x + -4 + -4x

Combine like terms: 40 + -4 = 36
36 + 40x + -4x + x2 = 4 + 4x + -4 + -4x

Combine like terms: 40x + -4x = 36x
36 + 36x + x2 = 4 + 4x + -4 + -4x

Reorder the terms:
36 + 36x + x2 = 4 + -4 + 4x + -4x

Combine like terms: 4 + -4 = 0
36 + 36x + x2 = 0 + 4x + -4x
36 + 36x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
36 + 36x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + 36x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + 36x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 36x + x2 = 0 + -36
36x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
36x + x2 = -36

The x term is 36x.  Take half its coefficient (18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
36x + 324 + x2 = -36 + 324

Reorder the terms:
324 + 36x + x2 = -36 + 324

Combine like terms: -36 + 324 = 288
324 + 36x + x2 = 288

Factor a perfect square on the left side:
(x + 18)(x + 18) = 288

Calculate the square root of the right side: 16.970562748

Break this problem into two subproblems by setting 
(x + 18) equal to 16.970562748 and -16.970562748.

Subproblem 1

x + 18 = 16.970562748 Simplifying x + 18 = 16.970562748 Reorder the terms: 18 + x = 16.970562748 Solving 18 + x = 16.970562748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 16.970562748 + -18 Combine like terms: 18 + -18 = 0 0 + x = 16.970562748 + -18 x = 16.970562748 + -18 Combine like terms: 16.970562748 + -18 = -1.029437252 x = -1.029437252 Simplifying x = -1.029437252

Subproblem 2

x + 18 = -16.970562748 Simplifying x + 18 = -16.970562748 Reorder the terms: 18 + x = -16.970562748 Solving 18 + x = -16.970562748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -16.970562748 + -18 Combine like terms: 18 + -18 = 0 0 + x = -16.970562748 + -18 x = -16.970562748 + -18 Combine like terms: -16.970562748 + -18 = -34.970562748 x = -34.970562748 Simplifying x = -34.970562748

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.029437252, -34.970562748}

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