x^2+40x+400=12

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Solution for x^2+40x+400=12 equation:


Simplifying
x2 + 40x + 400 = 12

Reorder the terms:
400 + 40x + x2 = 12

Solving
400 + 40x + x2 = 12

Solving for variable 'x'.

Reorder the terms:
400 + -12 + 40x + x2 = 12 + -12

Combine like terms: 400 + -12 = 388
388 + 40x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
388 + 40x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-388' to each side of the equation.
388 + 40x + -388 + x2 = 0 + -388

Reorder the terms:
388 + -388 + 40x + x2 = 0 + -388

Combine like terms: 388 + -388 = 0
0 + 40x + x2 = 0 + -388
40x + x2 = 0 + -388

Combine like terms: 0 + -388 = -388
40x + x2 = -388

The x term is 40x.  Take half its coefficient (20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
40x + 400 + x2 = -388 + 400

Reorder the terms:
400 + 40x + x2 = -388 + 400

Combine like terms: -388 + 400 = 12
400 + 40x + x2 = 12

Factor a perfect square on the left side:
(x + 20)(x + 20) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + 20) equal to 3.464101615 and -3.464101615.

Subproblem 1

x + 20 = 3.464101615 Simplifying x + 20 = 3.464101615 Reorder the terms: 20 + x = 3.464101615 Solving 20 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 3.464101615 + -20 Combine like terms: 20 + -20 = 0 0 + x = 3.464101615 + -20 x = 3.464101615 + -20 Combine like terms: 3.464101615 + -20 = -16.535898385 x = -16.535898385 Simplifying x = -16.535898385

Subproblem 2

x + 20 = -3.464101615 Simplifying x + 20 = -3.464101615 Reorder the terms: 20 + x = -3.464101615 Solving 20 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -3.464101615 + -20 Combine like terms: 20 + -20 = 0 0 + x = -3.464101615 + -20 x = -3.464101615 + -20 Combine like terms: -3.464101615 + -20 = -23.464101615 x = -23.464101615 Simplifying x = -23.464101615

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-16.535898385, -23.464101615}

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