-4x(x-26)=-200

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Solution for -4x(x-26)=-200 equation: 


Simplifying
-4x(x + -26) = -200

Reorder the terms:
-4x(-26 + x) = -200
(-26 * -4x + x * -4x) = -200
(104x + -4x2) = -200

Solving
104x + -4x2 = -200

Solving for variable 'x'.

Reorder the terms:
200 + 104x + -4x2 = -200 + 200

Combine like terms: -200 + 200 = 0
200 + 104x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(50 + 26x + -1x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(50 + 26x + -1x2)' equal to zero and attempt to solve:

Simplifying
50 + 26x + -1x2 = 0

Solving
50 + 26x + -1x2 = 0

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

Divide each side by '-1'.
-50 + -26x + x2 = 0

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -26x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + -26x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -26x + x2 = 0 + 50
-26x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
-26x + x2 = 50

The x term is -26x.  Take half its coefficient (-13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
-26x + 169 + x2 = 50 + 169

Reorder the terms:
169 + -26x + x2 = 50 + 169

Combine like terms: 50 + 169 = 219
169 + -26x + x2 = 219

Factor a perfect square on the left side:
(x + -13)(x + -13) = 219

Calculate the square root of the right side: 14.798648587

Break this problem into two subproblems by setting 
(x + -13) equal to 14.798648587 and -14.798648587.


Subproblem 1
x + -13 = 14.798648587

Simplifying
x + -13 = 14.798648587

Reorder the terms:
-13 + x = 14.798648587

Solving
-13 + x = 14.798648587

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '13' to each side of the equation.
-13 + 13 + x = 14.798648587 + 13

Combine like terms: -13 + 13 = 0
0 + x = 14.798648587 + 13
x = 14.798648587 + 13

Combine like terms: 14.798648587 + 13 = 27.798648587
x = 27.798648587

Simplifying
x = 27.798648587


Subproblem 2
x + -13 = -14.798648587

Simplifying
x + -13 = -14.798648587

Reorder the terms:
-13 + x = -14.798648587

Solving
-13 + x = -14.798648587

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '13' to each side of the equation.
-13 + 13 + x = -14.798648587 + 13

Combine like terms: -13 + 13 = 0
0 + x = -14.798648587 + 13
x = -14.798648587 + 13

Combine like terms: -14.798648587 + 13 = -1.798648587
x = -1.798648587

Simplifying
x = -1.798648587


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {27.798648587, -1.798648587}
Solution
x = {27.798648587, -1.798648587}

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