x^2+40x+100=

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Solution for x^2+40x+100= equation:


Simplifying
x2 + 40x + 100 = 0

Reorder the terms:
100 + 40x + x2 = 0

Solving
100 + 40x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + 40x + -100 + x2 = 0 + -100

Reorder the terms:
100 + -100 + 40x + x2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + 40x + x2 = 0 + -100
40x + x2 = 0 + -100

Combine like terms: 0 + -100 = -100
40x + x2 = -100

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 = -100 + 400

Reorder the terms:
400 + 40x + x2 = -100 + 400

Combine like terms: -100 + 400 = 300
400 + 40x + x2 = 300

Factor a perfect square on the left side:
(x + 20)(x + 20) = 300

Calculate the square root of the right side: 17.320508076

Break this problem into two subproblems by setting 
(x + 20) equal to 17.320508076 and -17.320508076.

Subproblem 1

x + 20 = 17.320508076 Simplifying x + 20 = 17.320508076 Reorder the terms: 20 + x = 17.320508076 Solving 20 + x = 17.320508076 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 = 17.320508076 + -20 Combine like terms: 20 + -20 = 0 0 + x = 17.320508076 + -20 x = 17.320508076 + -20 Combine like terms: 17.320508076 + -20 = -2.679491924 x = -2.679491924 Simplifying x = -2.679491924

Subproblem 2

x + 20 = -17.320508076 Simplifying x + 20 = -17.320508076 Reorder the terms: 20 + x = -17.320508076 Solving 20 + x = -17.320508076 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 = -17.320508076 + -20 Combine like terms: 20 + -20 = 0 0 + x = -17.320508076 + -20 x = -17.320508076 + -20 Combine like terms: -17.320508076 + -20 = -37.320508076 x = -37.320508076 Simplifying x = -37.320508076

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.679491924, -37.320508076}

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