-5x^2+165x-30=0

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Solution for -5x^2+165x-30=0 equation:


Simplifying
-5x2 + 165x + -30 = 0

Reorder the terms:
-30 + 165x + -5x2 = 0

Solving
-30 + 165x + -5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + 33x + -1x2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-6 + 33x + -1x2)' equal to zero and attempt to solve: Simplifying -6 + 33x + -1x2 = 0 Solving -6 + 33x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6 + -33x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -33x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -33x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -33x + x2 = 0 + -6 -33x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -33x + x2 = -6 The x term is -33x. Take half its coefficient (-16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. -33x + 272.25 + x2 = -6 + 272.25 Reorder the terms: 272.25 + -33x + x2 = -6 + 272.25 Combine like terms: -6 + 272.25 = 266.25 272.25 + -33x + x2 = 266.25 Factor a perfect square on the left side: (x + -16.5)(x + -16.5) = 266.25 Calculate the square root of the right side: 16.317168872 Break this problem into two subproblems by setting (x + -16.5) equal to 16.317168872 and -16.317168872.

Subproblem 1

x + -16.5 = 16.317168872 Simplifying x + -16.5 = 16.317168872 Reorder the terms: -16.5 + x = 16.317168872 Solving -16.5 + x = 16.317168872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = 16.317168872 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = 16.317168872 + 16.5 x = 16.317168872 + 16.5 Combine like terms: 16.317168872 + 16.5 = 32.817168872 x = 32.817168872 Simplifying x = 32.817168872

Subproblem 2

x + -16.5 = -16.317168872 Simplifying x + -16.5 = -16.317168872 Reorder the terms: -16.5 + x = -16.317168872 Solving -16.5 + x = -16.317168872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = -16.317168872 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = -16.317168872 + 16.5 x = -16.317168872 + 16.5 Combine like terms: -16.317168872 + 16.5 = 0.182831128 x = 0.182831128 Simplifying x = 0.182831128

Solution

The solution to the problem is based on the solutions from the subproblems. x = {32.817168872, 0.182831128}

Solution

x = {32.817168872, 0.182831128}

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