# 4x(x-2)=100

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## Solution for 4x(x-2)=100 equation:

Simplifying
4x(x + -2) = 100
Reorder the terms:
4x(-2 + x) = 100
(-2 * 4x + x * 4x) = 100
(-8x + 4x2) = 100
Solving
-8x + 4x2 = 100
Solving for variable 'x'.
Reorder the terms:
-100 + -8x + 4x2 = 100 + -100
Combine like terms: 100 + -100 = 0
-100 + -8x + 4x2 = 0
Factor out the Greatest Common Factor (GCF), '4'.
4(-25 + -2x + x2) = 0
Ignore the factor 4.
Subproblem 1Set the factor '(-25 + -2x + x2)' equal to zero and attempt to solve:
Simplifying
-25 + -2x + x2 = 0
Solving
-25 + -2x + x2 = 0
Begin completing the square.
Move the constant term to the right:
Add '25' to each side of the equation.
-25 + -2x + 25 + x2 = 0 + 25
Reorder the terms:
-25 + 25 + -2x + x2 = 0 + 25
Combine like terms: -25 + 25 = 0
0 + -2x + x2 = 0 + 25
-2x + x2 = 0 + 25
Combine like terms: 0 + 25 = 25
-2x + x2 = 25
The x term is -2x. Take half its coefficient (-1).
Square it (1) and add it to both sides.
Add '1' to each side of the equation.
-2x + 1 + x2 = 25 + 1
Reorder the terms:
1 + -2x + x2 = 25 + 1
Combine like terms: 25 + 1 = 26
1 + -2x + x2 = 26
Factor a perfect square on the left side:
(x + -1)(x + -1) = 26
Calculate the square root of the right side: 5.099019514
Break this problem into two subproblems by setting
(x + -1) equal to 5.099019514 and -5.099019514.
Subproblem 1x + -1 = 5.099019514
Simplifying
x + -1 = 5.099019514
Reorder the terms:
-1 + x = 5.099019514
Solving
-1 + x = 5.099019514
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '1' to each side of the equation.
-1 + 1 + x = 5.099019514 + 1
Combine like terms: -1 + 1 = 0
0 + x = 5.099019514 + 1
x = 5.099019514 + 1
Combine like terms: 5.099019514 + 1 = 6.099019514
x = 6.099019514
Simplifying
x = 6.099019514
Subproblem 2x + -1 = -5.099019514
Simplifying
x + -1 = -5.099019514
Reorder the terms:
-1 + x = -5.099019514
Solving
-1 + x = -5.099019514
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '1' to each side of the equation.
-1 + 1 + x = -5.099019514 + 1
Combine like terms: -1 + 1 = 0
0 + x = -5.099019514 + 1
x = -5.099019514 + 1
Combine like terms: -5.099019514 + 1 = -4.099019514
x = -4.099019514
Simplifying
x = -4.099019514
SolutionThe solution to the problem is based on the solutions
from the subproblems.
x = {6.099019514, -4.099019514}Solutionx = {6.099019514, -4.099019514}`