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Simplifying 6x2 + -12x = 80 Reorder the terms: -12x + 6x2 = 80 Solving -12x + 6x2 = 80 Solving for variable 'x'. Reorder the terms: -80 + -12x + 6x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + -12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-40 + -6x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-40 + -6x + 3x2)' equal to zero and attempt to solve: Simplifying -40 + -6x + 3x2 = 0 Solving -40 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -13.33333333 + -2x + x2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + -2x + 13.33333333 + x2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + -2x + x2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + -2x + x2 = 0 + 13.33333333 -2x + x2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 -2x + x2 = 13.33333333 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 13.33333333 + 1 Reorder the terms: 1 + -2x + x2 = 13.33333333 + 1 Combine like terms: 13.33333333 + 1 = 14.33333333 1 + -2x + x2 = 14.33333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 14.33333333 Calculate the square root of the right side: 3.785938897 Break this problem into two subproblems by setting (x + -1) equal to 3.785938897 and -3.785938897.Subproblem 1
x + -1 = 3.785938897 Simplifying x + -1 = 3.785938897 Reorder the terms: -1 + x = 3.785938897 Solving -1 + x = 3.785938897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.785938897 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.785938897 + 1 x = 3.785938897 + 1 Combine like terms: 3.785938897 + 1 = 4.785938897 x = 4.785938897 Simplifying x = 4.785938897Subproblem 2
x + -1 = -3.785938897 Simplifying x + -1 = -3.785938897 Reorder the terms: -1 + x = -3.785938897 Solving -1 + x = -3.785938897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.785938897 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.785938897 + 1 x = -3.785938897 + 1 Combine like terms: -3.785938897 + 1 = -2.785938897 x = -2.785938897 Simplifying x = -2.785938897Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.785938897, -2.785938897}Solution
x = {4.785938897, -2.785938897}
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