80+20x=140x-5x^2

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Solution for 80+20x=140x-5x^2 equation:


Simplifying
80 + 20x = 140x + -5x2

Solving
80 + 20x = 140x + -5x2

Solving for variable 'x'.

Combine like terms: 20x + -140x = -120x
80 + -120x + 5x2 = 140x + -5x2 + -140x + 5x2

Reorder the terms:
80 + -120x + 5x2 = 140x + -140x + -5x2 + 5x2

Combine like terms: 140x + -140x = 0
80 + -120x + 5x2 = 0 + -5x2 + 5x2
80 + -120x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
80 + -120x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(16 + -24x + x2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(16 + -24x + x2)' equal to zero and attempt to solve: Simplifying 16 + -24x + x2 = 0 Solving 16 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -24x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -24x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -24x + x2 = 0 + -16 -24x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -24x + x2 = -16 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -16 + 144 Reorder the terms: 144 + -24x + x2 = -16 + 144 Combine like terms: -16 + 144 = 128 144 + -24x + x2 = 128 Factor a perfect square on the left side: (x + -12)(x + -12) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (x + -12) equal to 11.313708499 and -11.313708499.

Subproblem 1

x + -12 = 11.313708499 Simplifying x + -12 = 11.313708499 Reorder the terms: -12 + x = 11.313708499 Solving -12 + x = 11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 11.313708499 + 12 Combine like terms: -12 + 12 = 0 0 + x = 11.313708499 + 12 x = 11.313708499 + 12 Combine like terms: 11.313708499 + 12 = 23.313708499 x = 23.313708499 Simplifying x = 23.313708499

Subproblem 2

x + -12 = -11.313708499 Simplifying x + -12 = -11.313708499 Reorder the terms: -12 + x = -11.313708499 Solving -12 + x = -11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -11.313708499 + 12 Combine like terms: -12 + 12 = 0 0 + x = -11.313708499 + 12 x = -11.313708499 + 12 Combine like terms: -11.313708499 + 12 = 0.686291501 x = 0.686291501 Simplifying x = 0.686291501

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.313708499, 0.686291501}

Solution

x = {23.313708499, 0.686291501}

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