16=x^2+4x

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Solution for 16=x^2+4x equation:


Simplifying
16 = x2 + 4x

Reorder the terms:
16 = 4x + x2

Solving
16 = 4x + x2

Solving for variable 'x'.

Reorder the terms:
16 + -4x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
16 + -4x + -1x2 = 0 + x2 + -1x2
16 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16 + -4x + -1x2 = 0

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

Divide each side by '-1'.
-16 + 4x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 4x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 4x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 4x + x2 = 0 + 16
4x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
4x + x2 = 16

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 = 16 + 4

Reorder the terms:
4 + 4x + x2 = 16 + 4

Combine like terms: 16 + 4 = 20
4 + 4x + x2 = 20

Factor a perfect square on the left side:
(x + 2)(x + 2) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x + 2) equal to 4.472135955 and -4.472135955.

Subproblem 1

x + 2 = 4.472135955 Simplifying x + 2 = 4.472135955 Reorder the terms: 2 + x = 4.472135955 Solving 2 + x = 4.472135955 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 = 4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.472135955 + -2 x = 4.472135955 + -2 Combine like terms: 4.472135955 + -2 = 2.472135955 x = 2.472135955 Simplifying x = 2.472135955

Subproblem 2

x + 2 = -4.472135955 Simplifying x + 2 = -4.472135955 Reorder the terms: 2 + x = -4.472135955 Solving 2 + x = -4.472135955 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 = -4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.472135955 + -2 x = -4.472135955 + -2 Combine like terms: -4.472135955 + -2 = -6.472135955 x = -6.472135955 Simplifying x = -6.472135955

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.472135955, -6.472135955}

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