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 1

Set 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 1

x + -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 2

x + -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

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.099019514, -4.099019514}

Solution

x = {6.099019514, -4.099019514}

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