x^2+16x+16=4x-5

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Solution for x^2+16x+16=4x-5 equation:


Simplifying
x2 + 16x + 16 = 4x + -5

Reorder the terms:
16 + 16x + x2 = 4x + -5

Reorder the terms:
16 + 16x + x2 = -5 + 4x

Solving
16 + 16x + x2 = -5 + 4x

Solving for variable 'x'.

Reorder the terms:
16 + 5 + 16x + -4x + x2 = -5 + 4x + 5 + -4x

Combine like terms: 16 + 5 = 21
21 + 16x + -4x + x2 = -5 + 4x + 5 + -4x

Combine like terms: 16x + -4x = 12x
21 + 12x + x2 = -5 + 4x + 5 + -4x

Reorder the terms:
21 + 12x + x2 = -5 + 5 + 4x + -4x

Combine like terms: -5 + 5 = 0
21 + 12x + x2 = 0 + 4x + -4x
21 + 12x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
21 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + 12x + -21 + x2 = 0 + -21

Reorder the terms:
21 + -21 + 12x + x2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 12x + x2 = 0 + -21
12x + x2 = 0 + -21

Combine like terms: 0 + -21 = -21
12x + x2 = -21

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = -21 + 36

Reorder the terms:
36 + 12x + x2 = -21 + 36

Combine like terms: -21 + 36 = 15
36 + 12x + x2 = 15

Factor a perfect square on the left side:
(x + 6)(x + 6) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + 6) equal to 3.872983346 and -3.872983346.

Subproblem 1

x + 6 = 3.872983346 Simplifying x + 6 = 3.872983346 Reorder the terms: 6 + x = 3.872983346 Solving 6 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 3.872983346 + -6 Combine like terms: 6 + -6 = 0 0 + x = 3.872983346 + -6 x = 3.872983346 + -6 Combine like terms: 3.872983346 + -6 = -2.127016654 x = -2.127016654 Simplifying x = -2.127016654

Subproblem 2

x + 6 = -3.872983346 Simplifying x + 6 = -3.872983346 Reorder the terms: 6 + x = -3.872983346 Solving 6 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -3.872983346 + -6 Combine like terms: 6 + -6 = 0 0 + x = -3.872983346 + -6 x = -3.872983346 + -6 Combine like terms: -3.872983346 + -6 = -9.872983346 x = -9.872983346 Simplifying x = -9.872983346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.127016654, -9.872983346}

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