x(x-4)-20=0

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Solution for x(x-4)-20=0 equation:


Simplifying
x(x + -4) + -20 = 0

Reorder the terms:
x(-4 + x) + -20 = 0
(-4 * x + x * x) + -20 = 0
(-4x + x2) + -20 = 0

Reorder the terms:
-20 + -4x + x2 = 0

Solving
-20 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -4x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -4x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -4x + x2 = 0 + 20
-4x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-4x + x2 = 20

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 = 20 + 4

Reorder the terms:
4 + -4x + x2 = 20 + 4

Combine like terms: 20 + 4 = 24
4 + -4x + x2 = 24

Factor a perfect square on the left side:
(x + -2)(x + -2) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + -2) equal to 4.898979486 and -4.898979486.

Subproblem 1

x + -2 = 4.898979486 Simplifying x + -2 = 4.898979486 Reorder the terms: -2 + x = 4.898979486 Solving -2 + x = 4.898979486 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 = 4.898979486 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.898979486 + 2 x = 4.898979486 + 2 Combine like terms: 4.898979486 + 2 = 6.898979486 x = 6.898979486 Simplifying x = 6.898979486

Subproblem 2

x + -2 = -4.898979486 Simplifying x + -2 = -4.898979486 Reorder the terms: -2 + x = -4.898979486 Solving -2 + x = -4.898979486 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 = -4.898979486 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.898979486 + 2 x = -4.898979486 + 2 Combine like terms: -4.898979486 + 2 = -2.898979486 x = -2.898979486 Simplifying x = -2.898979486

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.898979486, -2.898979486}

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