6x+13=x^2+4x+4

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Solution for 6x+13=x^2+4x+4 equation:


Simplifying
6x + 13 = x2 + 4x + 4

Reorder the terms:
13 + 6x = x2 + 4x + 4

Reorder the terms:
13 + 6x = 4 + 4x + x2

Solving
13 + 6x = 4 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
13 + -4 + 6x + -4x + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: 13 + -4 = 9
9 + 6x + -4x + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: 6x + -4x = 2x
9 + 2x + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Reorder the terms:
9 + 2x + -1x2 = 4 + -4 + 4x + -4x + x2 + -1x2

Combine like terms: 4 + -4 = 0
9 + 2x + -1x2 = 0 + 4x + -4x + x2 + -1x2
9 + 2x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
9 + 2x + -1x2 = 0 + x2 + -1x2
9 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
9 + 2x + -1x2 = 0

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

Divide each side by '-1'.
-9 + -2x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -2x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -2x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x + x2 = 0 + 9
-2x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-2x + x2 = 9

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 = 9 + 1

Reorder the terms:
1 + -2x + x2 = 9 + 1

Combine like terms: 9 + 1 = 10
1 + -2x + x2 = 10

Factor a perfect square on the left side:
(x + -1)(x + -1) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + -1) equal to 3.16227766 and -3.16227766.

Subproblem 1

x + -1 = 3.16227766 Simplifying x + -1 = 3.16227766 Reorder the terms: -1 + x = 3.16227766 Solving -1 + x = 3.16227766 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 = 3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.16227766 + 1 x = 3.16227766 + 1 Combine like terms: 3.16227766 + 1 = 4.16227766 x = 4.16227766 Simplifying x = 4.16227766

Subproblem 2

x + -1 = -3.16227766 Simplifying x + -1 = -3.16227766 Reorder the terms: -1 + x = -3.16227766 Solving -1 + x = -3.16227766 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 = -3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.16227766 + 1 x = -3.16227766 + 1 Combine like terms: -3.16227766 + 1 = -2.16227766 x = -2.16227766 Simplifying x = -2.16227766

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.16227766, -2.16227766}

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