4x^2-54x+80=0

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Solution for 4x^2-54x+80=0 equation:


Simplifying
4x2 + -54x + 80 = 0

Reorder the terms:
80 + -54x + 4x2 = 0

Solving
80 + -54x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(40 + -27x + 2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(40 + -27x + 2x2)' equal to zero and attempt to solve: Simplifying 40 + -27x + 2x2 = 0 Solving 40 + -27x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 20 + -13.5x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -13.5x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -13.5x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -13.5x + x2 = 0 + -20 -13.5x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -13.5x + x2 = -20 The x term is -13.5x. Take half its coefficient (-6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. -13.5x + 45.5625 + x2 = -20 + 45.5625 Reorder the terms: 45.5625 + -13.5x + x2 = -20 + 45.5625 Combine like terms: -20 + 45.5625 = 25.5625 45.5625 + -13.5x + x2 = 25.5625 Factor a perfect square on the left side: (x + -6.75)(x + -6.75) = 25.5625 Calculate the square root of the right side: 5.055937104 Break this problem into two subproblems by setting (x + -6.75) equal to 5.055937104 and -5.055937104.

Subproblem 1

x + -6.75 = 5.055937104 Simplifying x + -6.75 = 5.055937104 Reorder the terms: -6.75 + x = 5.055937104 Solving -6.75 + x = 5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = 5.055937104 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = 5.055937104 + 6.75 x = 5.055937104 + 6.75 Combine like terms: 5.055937104 + 6.75 = 11.805937104 x = 11.805937104 Simplifying x = 11.805937104

Subproblem 2

x + -6.75 = -5.055937104 Simplifying x + -6.75 = -5.055937104 Reorder the terms: -6.75 + x = -5.055937104 Solving -6.75 + x = -5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = -5.055937104 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = -5.055937104 + 6.75 x = -5.055937104 + 6.75 Combine like terms: -5.055937104 + 6.75 = 1.694062896 x = 1.694062896 Simplifying x = 1.694062896

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.805937104, 1.694062896}

Solution

x = {11.805937104, 1.694062896}

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