x^2+20x=-7

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Solution for x^2+20x=-7 equation:


Simplifying
x2 + 20x = -7

Reorder the terms:
20x + x2 = -7

Solving
20x + x2 = -7

Solving for variable 'x'.

Reorder the terms:
7 + 20x + x2 = -7 + 7

Combine like terms: -7 + 7 = 0
7 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 20x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 20x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 20x + x2 = 0 + -7
20x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
20x + x2 = -7

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 = -7 + 100

Reorder the terms:
100 + 20x + x2 = -7 + 100

Combine like terms: -7 + 100 = 93
100 + 20x + x2 = 93

Factor a perfect square on the left side:
(x + 10)(x + 10) = 93

Calculate the square root of the right side: 9.643650761

Break this problem into two subproblems by setting 
(x + 10) equal to 9.643650761 and -9.643650761.

Subproblem 1

x + 10 = 9.643650761 Simplifying x + 10 = 9.643650761 Reorder the terms: 10 + x = 9.643650761 Solving 10 + x = 9.643650761 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 = 9.643650761 + -10 Combine like terms: 10 + -10 = 0 0 + x = 9.643650761 + -10 x = 9.643650761 + -10 Combine like terms: 9.643650761 + -10 = -0.356349239 x = -0.356349239 Simplifying x = -0.356349239

Subproblem 2

x + 10 = -9.643650761 Simplifying x + 10 = -9.643650761 Reorder the terms: 10 + x = -9.643650761 Solving 10 + x = -9.643650761 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 = -9.643650761 + -10 Combine like terms: 10 + -10 = 0 0 + x = -9.643650761 + -10 x = -9.643650761 + -10 Combine like terms: -9.643650761 + -10 = -19.643650761 x = -19.643650761 Simplifying x = -19.643650761

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.356349239, -19.643650761}

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