4x(x-4)=17

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Solution for 4x(x-4)=17 equation: 


Simplifying
4x(x + -4) = 17

Reorder the terms:
4x(-4 + x) = 17
(-4 * 4x + x * 4x) = 17
(-16x + 4x2) = 17

Solving
-16x + 4x2 = 17

Solving for variable 'x'.

Reorder the terms:
-17 + -16x + 4x2 = 17 + -17

Combine like terms: 17 + -17 = 0
-17 + -16x + 4x2 = 0

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

Divide each side by '4'.
-4.25 + -4x + x2 = 0

Move the constant term to the right:

Add '4.25' to each side of the equation.
-4.25 + -4x + 4.25 + x2 = 0 + 4.25

Reorder the terms:
-4.25 + 4.25 + -4x + x2 = 0 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + -4x + x2 = 0 + 4.25
-4x + x2 = 0 + 4.25

Combine like terms: 0 + 4.25 = 4.25
-4x + x2 = 4.25

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 = 4.25 + 4

Reorder the terms:
4 + -4x + x2 = 4.25 + 4

Combine like terms: 4.25 + 4 = 8.25
4 + -4x + x2 = 8.25

Factor a perfect square on the left side:
(x + -2)(x + -2) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x + -2) equal to 2.872281323 and -2.872281323.


Subproblem 1
x + -2 = 2.872281323

Simplifying
x + -2 = 2.872281323

Reorder the terms:
-2 + x = 2.872281323

Solving
-2 + x = 2.872281323

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 = 2.872281323 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.872281323 + 2
x = 2.872281323 + 2

Combine like terms: 2.872281323 + 2 = 4.872281323
x = 4.872281323

Simplifying
x = 4.872281323


Subproblem 2
x + -2 = -2.872281323

Simplifying
x + -2 = -2.872281323

Reorder the terms:
-2 + x = -2.872281323

Solving
-2 + x = -2.872281323

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 = -2.872281323 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.872281323 + 2
x = -2.872281323 + 2

Combine like terms: -2.872281323 + 2 = -0.872281323
x = -0.872281323

Simplifying
x = -0.872281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.872281323, -0.872281323}

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