0=x^2+4x-55

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Solution for 0=x^2+4x-55 equation:


Simplifying
0 = x2 + 4x + -55

Reorder the terms:
0 = -55 + 4x + x2

Solving
0 = -55 + 4x + x2

Solving for variable 'x'.

Combine like terms: 0 + 55 = 55
55 + -4x + -1x2 = -55 + 4x + x2 + 55 + -4x + -1x2

Reorder the terms:
55 + -4x + -1x2 = -55 + 55 + 4x + -4x + x2 + -1x2

Combine like terms: -55 + 55 = 0
55 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2
55 + -4x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
55 + -4x + -1x2 = 0 + x2 + -1x2
55 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
55 + -4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-55 + 4x + x2 = 0

Move the constant term to the right:

Add '55' to each side of the equation.
-55 + 4x + 55 + x2 = 0 + 55

Reorder the terms:
-55 + 55 + 4x + x2 = 0 + 55

Combine like terms: -55 + 55 = 0
0 + 4x + x2 = 0 + 55
4x + x2 = 0 + 55

Combine like terms: 0 + 55 = 55
4x + x2 = 55

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 55 + 4

Reorder the terms:
4 + 4x + x2 = 55 + 4

Combine like terms: 55 + 4 = 59
4 + 4x + x2 = 59

Factor a perfect square on the left side:
(x + 2)(x + 2) = 59

Calculate the square root of the right side: 7.681145748

Break this problem into two subproblems by setting 
(x + 2) equal to 7.681145748 and -7.681145748.

Subproblem 1

x + 2 = 7.681145748 Simplifying x + 2 = 7.681145748 Reorder the terms: 2 + x = 7.681145748 Solving 2 + x = 7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 7.681145748 + -2 Combine like terms: 2 + -2 = 0 0 + x = 7.681145748 + -2 x = 7.681145748 + -2 Combine like terms: 7.681145748 + -2 = 5.681145748 x = 5.681145748 Simplifying x = 5.681145748

Subproblem 2

x + 2 = -7.681145748 Simplifying x + 2 = -7.681145748 Reorder the terms: 2 + x = -7.681145748 Solving 2 + x = -7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -7.681145748 + -2 Combine like terms: 2 + -2 = 0 0 + x = -7.681145748 + -2 x = -7.681145748 + -2 Combine like terms: -7.681145748 + -2 = -9.681145748 x = -9.681145748 Simplifying x = -9.681145748

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.681145748, -9.681145748}

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