0=6x^2-36x-110

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Solution for 0=6x^2-36x-110 equation:


Simplifying
0 = 6x2 + -36x + -110

Reorder the terms:
0 = -110 + -36x + 6x2

Solving
0 = -110 + -36x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + 110 = 110
110 + 36x + -6x2 = -110 + -36x + 6x2 + 110 + 36x + -6x2

Reorder the terms:
110 + 36x + -6x2 = -110 + 110 + -36x + 36x + 6x2 + -6x2

Combine like terms: -110 + 110 = 0
110 + 36x + -6x2 = 0 + -36x + 36x + 6x2 + -6x2
110 + 36x + -6x2 = -36x + 36x + 6x2 + -6x2

Combine like terms: -36x + 36x = 0
110 + 36x + -6x2 = 0 + 6x2 + -6x2
110 + 36x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
110 + 36x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(55 + 18x + -3x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(55 + 18x + -3x2)' equal to zero and attempt to solve: Simplifying 55 + 18x + -3x2 = 0 Solving 55 + 18x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -18.33333333 + -6x + x2 = 0 Move the constant term to the right: Add '18.33333333' to each side of the equation. -18.33333333 + -6x + 18.33333333 + x2 = 0 + 18.33333333 Reorder the terms: -18.33333333 + 18.33333333 + -6x + x2 = 0 + 18.33333333 Combine like terms: -18.33333333 + 18.33333333 = 0.00000000 0.00000000 + -6x + x2 = 0 + 18.33333333 -6x + x2 = 0 + 18.33333333 Combine like terms: 0 + 18.33333333 = 18.33333333 -6x + x2 = 18.33333333 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 18.33333333 + 9 Reorder the terms: 9 + -6x + x2 = 18.33333333 + 9 Combine like terms: 18.33333333 + 9 = 27.33333333 9 + -6x + x2 = 27.33333333 Factor a perfect square on the left side: (x + -3)(x + -3) = 27.33333333 Calculate the square root of the right side: 5.228129047 Break this problem into two subproblems by setting (x + -3) equal to 5.228129047 and -5.228129047.

Subproblem 1

x + -3 = 5.228129047 Simplifying x + -3 = 5.228129047 Reorder the terms: -3 + x = 5.228129047 Solving -3 + x = 5.228129047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 5.228129047 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.228129047 + 3 x = 5.228129047 + 3 Combine like terms: 5.228129047 + 3 = 8.228129047 x = 8.228129047 Simplifying x = 8.228129047

Subproblem 2

x + -3 = -5.228129047 Simplifying x + -3 = -5.228129047 Reorder the terms: -3 + x = -5.228129047 Solving -3 + x = -5.228129047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -5.228129047 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.228129047 + 3 x = -5.228129047 + 3 Combine like terms: -5.228129047 + 3 = -2.228129047 x = -2.228129047 Simplifying x = -2.228129047

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.228129047, -2.228129047}

Solution

x = {8.228129047, -2.228129047}

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