x^2+2x-54.60=0

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Solution for x^2+2x-54.60=0 equation:


Simplifying
x2 + 2x + -54.60 = 0

Reorder the terms:
-54.60 + 2x + x2 = 0

Solving
-54.60 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '54.60' to each side of the equation.
-54.60 + 2x + 54.60 + x2 = 0 + 54.60

Reorder the terms:
-54.60 + 54.60 + 2x + x2 = 0 + 54.60

Combine like terms: -54.60 + 54.60 = 0.00
0.00 + 2x + x2 = 0 + 54.60
2x + x2 = 0 + 54.60

Combine like terms: 0 + 54.60 = 54.6
2x + x2 = 54.6

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 54.6 + 1

Reorder the terms:
1 + 2x + x2 = 54.6 + 1

Combine like terms: 54.6 + 1 = 55.6
1 + 2x + x2 = 55.6

Factor a perfect square on the left side:
(x + 1)(x + 1) = 55.6

Calculate the square root of the right side: 7.456540753

Break this problem into two subproblems by setting 
(x + 1) equal to 7.456540753 and -7.456540753.

Subproblem 1

x + 1 = 7.456540753 Simplifying x + 1 = 7.456540753 Reorder the terms: 1 + x = 7.456540753 Solving 1 + x = 7.456540753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 7.456540753 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.456540753 + -1 x = 7.456540753 + -1 Combine like terms: 7.456540753 + -1 = 6.456540753 x = 6.456540753 Simplifying x = 6.456540753

Subproblem 2

x + 1 = -7.456540753 Simplifying x + 1 = -7.456540753 Reorder the terms: 1 + x = -7.456540753 Solving 1 + x = -7.456540753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -7.456540753 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.456540753 + -1 x = -7.456540753 + -1 Combine like terms: -7.456540753 + -1 = -8.456540753 x = -8.456540753 Simplifying x = -8.456540753

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.456540753, -8.456540753}

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