80=(2x-5)x

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Solution for 80=(2x-5)x equation:


Simplifying
80 = (2x + -5) * x

Reorder the terms:
80 = (-5 + 2x) * x

Reorder the terms for easier multiplication:
80 = x(-5 + 2x)
80 = (-5 * x + 2x * x)
80 = (-5x + 2x2)

Solving
80 = -5x + 2x2

Solving for variable 'x'.

Reorder the terms:
80 + 5x + -2x2 = -5x + 5x + 2x2 + -2x2

Combine like terms: -5x + 5x = 0
80 + 5x + -2x2 = 0 + 2x2 + -2x2
80 + 5x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
80 + 5x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-40 + -2.5x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -2.5x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -2.5x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -2.5x + x2 = 0 + 40
-2.5x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-2.5x + x2 = 40

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 40 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 40 + 1.5625

Combine like terms: 40 + 1.5625 = 41.5625
1.5625 + -2.5x + x2 = 41.5625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 41.5625

Calculate the square root of the right side: 6.446898479

Break this problem into two subproblems by setting 
(x + -1.25) equal to 6.446898479 and -6.446898479.

Subproblem 1

x + -1.25 = 6.446898479 Simplifying x + -1.25 = 6.446898479 Reorder the terms: -1.25 + x = 6.446898479 Solving -1.25 + x = 6.446898479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 6.446898479 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 6.446898479 + 1.25 x = 6.446898479 + 1.25 Combine like terms: 6.446898479 + 1.25 = 7.696898479 x = 7.696898479 Simplifying x = 7.696898479

Subproblem 2

x + -1.25 = -6.446898479 Simplifying x + -1.25 = -6.446898479 Reorder the terms: -1.25 + x = -6.446898479 Solving -1.25 + x = -6.446898479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -6.446898479 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -6.446898479 + 1.25 x = -6.446898479 + 1.25 Combine like terms: -6.446898479 + 1.25 = -5.196898479 x = -5.196898479 Simplifying x = -5.196898479

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.696898479, -5.196898479}

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