80=x(x-4)

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Solution for 80=x(x-4) equation:


Simplifying
80 = x(x + -4)

Reorder the terms:
80 = x(-4 + x)
80 = (-4 * x + x * x)
80 = (-4x + x2)

Solving
80 = -4x + x2

Solving for variable 'x'.

Reorder the terms:
80 + 4x + -1x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
80 + 4x + -1x2 = 0 + x2 + -1x2
80 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
80 + 4x + -1x2 = 0

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

Divide each side by '-1'.
-80 + -4x + x2 = 0

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -4x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + -4x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -4x + x2 = 0 + 80
-4x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
-4x + x2 = 80

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 = 80 + 4

Reorder the terms:
4 + -4x + x2 = 80 + 4

Combine like terms: 80 + 4 = 84
4 + -4x + x2 = 84

Factor a perfect square on the left side:
(x + -2)(x + -2) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(x + -2) equal to 9.16515139 and -9.16515139.

Subproblem 1

x + -2 = 9.16515139 Simplifying x + -2 = 9.16515139 Reorder the terms: -2 + x = 9.16515139 Solving -2 + x = 9.16515139 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 = 9.16515139 + 2 Combine like terms: -2 + 2 = 0 0 + x = 9.16515139 + 2 x = 9.16515139 + 2 Combine like terms: 9.16515139 + 2 = 11.16515139 x = 11.16515139 Simplifying x = 11.16515139

Subproblem 2

x + -2 = -9.16515139 Simplifying x + -2 = -9.16515139 Reorder the terms: -2 + x = -9.16515139 Solving -2 + x = -9.16515139 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 = -9.16515139 + 2 Combine like terms: -2 + 2 = 0 0 + x = -9.16515139 + 2 x = -9.16515139 + 2 Combine like terms: -9.16515139 + 2 = -7.16515139 x = -7.16515139 Simplifying x = -7.16515139

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.16515139, -7.16515139}

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