x^2+20x=-6

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Solution for x^2+20x=-6 equation:


Simplifying
x2 + 20x = -6

Reorder the terms:
20x + x2 = -6

Solving
20x + x2 = -6

Solving for variable 'x'.

Reorder the terms:
6 + 20x + x2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 20x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 20x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 20x + x2 = 0 + -6
20x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
20x + x2 = -6

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -6 + 100

Reorder the terms:
100 + 20x + x2 = -6 + 100

Combine like terms: -6 + 100 = 94
100 + 20x + x2 = 94

Factor a perfect square on the left side:
(x + 10)(x + 10) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(x + 10) equal to 9.695359715 and -9.695359715.

Subproblem 1

x + 10 = 9.695359715 Simplifying x + 10 = 9.695359715 Reorder the terms: 10 + x = 9.695359715 Solving 10 + x = 9.695359715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 9.695359715 + -10 Combine like terms: 10 + -10 = 0 0 + x = 9.695359715 + -10 x = 9.695359715 + -10 Combine like terms: 9.695359715 + -10 = -0.304640285 x = -0.304640285 Simplifying x = -0.304640285

Subproblem 2

x + 10 = -9.695359715 Simplifying x + 10 = -9.695359715 Reorder the terms: 10 + x = -9.695359715 Solving 10 + x = -9.695359715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -9.695359715 + -10 Combine like terms: 10 + -10 = 0 0 + x = -9.695359715 + -10 x = -9.695359715 + -10 Combine like terms: -9.695359715 + -10 = -19.695359715 x = -19.695359715 Simplifying x = -19.695359715

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.304640285, -19.695359715}

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