84=(x-4)x

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Solution for 84=(x-4)x equation:


Simplifying
84 = (x + -4) * x

Reorder the terms:
84 = (-4 + x) * x

Reorder the terms for easier multiplication:
84 = x(-4 + x)
84 = (-4 * x + x * x)
84 = (-4x + x2)

Solving
84 = -4x + x2

Solving for variable 'x'.

Reorder the terms:
84 + 4x + -1x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
84 + 4x + -1x2 = 0 + x2 + -1x2
84 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
84 + 4x + -1x2 = 0

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

Divide each side by '-1'.
-84 + -4x + x2 = 0

Move the constant term to the right:

Add '84' to each side of the equation.
-84 + -4x + 84 + x2 = 0 + 84

Reorder the terms:
-84 + 84 + -4x + x2 = 0 + 84

Combine like terms: -84 + 84 = 0
0 + -4x + x2 = 0 + 84
-4x + x2 = 0 + 84

Combine like terms: 0 + 84 = 84
-4x + x2 = 84

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 = 84 + 4

Reorder the terms:
4 + -4x + x2 = 84 + 4

Combine like terms: 84 + 4 = 88
4 + -4x + x2 = 88

Factor a perfect square on the left side:
(x + -2)(x + -2) = 88

Calculate the square root of the right side: 9.38083152

Break this problem into two subproblems by setting 
(x + -2) equal to 9.38083152 and -9.38083152.

Subproblem 1

x + -2 = 9.38083152 Simplifying x + -2 = 9.38083152 Reorder the terms: -2 + x = 9.38083152 Solving -2 + x = 9.38083152 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 = 9.38083152 + 2 Combine like terms: -2 + 2 = 0 0 + x = 9.38083152 + 2 x = 9.38083152 + 2 Combine like terms: 9.38083152 + 2 = 11.38083152 x = 11.38083152 Simplifying x = 11.38083152

Subproblem 2

x + -2 = -9.38083152 Simplifying x + -2 = -9.38083152 Reorder the terms: -2 + x = -9.38083152 Solving -2 + x = -9.38083152 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 = -9.38083152 + 2 Combine like terms: -2 + 2 = 0 0 + x = -9.38083152 + 2 x = -9.38083152 + 2 Combine like terms: -9.38083152 + 2 = -7.38083152 x = -7.38083152 Simplifying x = -7.38083152

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.38083152, -7.38083152}

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