4(x+4)+1=x(x-4)

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Solution for 4(x+4)+1=x(x-4) equation:


Simplifying
4(x + 4) + 1 = x(x + -4)

Reorder the terms:
4(4 + x) + 1 = x(x + -4)
(4 * 4 + x * 4) + 1 = x(x + -4)
(16 + 4x) + 1 = x(x + -4)

Reorder the terms:
16 + 1 + 4x = x(x + -4)

Combine like terms: 16 + 1 = 17
17 + 4x = x(x + -4)

Reorder the terms:
17 + 4x = x(-4 + x)
17 + 4x = (-4 * x + x * x)
17 + 4x = (-4x + x2)

Solving
17 + 4x = -4x + x2

Solving for variable 'x'.

Combine like terms: 4x + 4x = 8x
17 + 8x + -1x2 = -4x + x2 + 4x + -1x2

Reorder the terms:
17 + 8x + -1x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
17 + 8x + -1x2 = 0 + x2 + -1x2
17 + 8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
17 + 8x + -1x2 = 0

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

Divide each side by '-1'.
-17 + -8x + x2 = 0

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -8x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + -8x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -8x + x2 = 0 + 17
-8x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
-8x + x2 = 17

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 17 + 16

Reorder the terms:
16 + -8x + x2 = 17 + 16

Combine like terms: 17 + 16 = 33
16 + -8x + x2 = 33

Factor a perfect square on the left side:
(x + -4)(x + -4) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(x + -4) equal to 5.744562647 and -5.744562647.

Subproblem 1

x + -4 = 5.744562647 Simplifying x + -4 = 5.744562647 Reorder the terms: -4 + x = 5.744562647 Solving -4 + x = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.744562647 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.744562647 + 4 x = 5.744562647 + 4 Combine like terms: 5.744562647 + 4 = 9.744562647 x = 9.744562647 Simplifying x = 9.744562647

Subproblem 2

x + -4 = -5.744562647 Simplifying x + -4 = -5.744562647 Reorder the terms: -4 + x = -5.744562647 Solving -4 + x = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.744562647 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.744562647 + 4 x = -5.744562647 + 4 Combine like terms: -5.744562647 + 4 = -1.744562647 x = -1.744562647 Simplifying x = -1.744562647

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.744562647, -1.744562647}

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