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Simplifying -2x2 + 12x = -6 Reorder the terms: 12x + -2x2 = -6 Solving 12x + -2x2 = -6 Solving for variable 'x'. Reorder the terms: 6 + 12x + -2x2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + 12x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 6x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying 3 + 6x + -1x2 = 0 Solving 3 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -6x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -6x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -6x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -6x + x2 = 0 + 3 -6x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -6x + x2 = 3 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 = 3 + 9 Reorder the terms: 9 + -6x + x2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + -6x + x2 = 12 Factor a perfect square on the left side: (x + -3)(x + -3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + -3) equal to 3.464101615 and -3.464101615.Subproblem 1
x + -3 = 3.464101615 Simplifying x + -3 = 3.464101615 Reorder the terms: -3 + x = 3.464101615 Solving -3 + x = 3.464101615 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 = 3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.464101615 + 3 x = 3.464101615 + 3 Combine like terms: 3.464101615 + 3 = 6.464101615 x = 6.464101615 Simplifying x = 6.464101615Subproblem 2
x + -3 = -3.464101615 Simplifying x + -3 = -3.464101615 Reorder the terms: -3 + x = -3.464101615 Solving -3 + x = -3.464101615 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 = -3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.464101615 + 3 x = -3.464101615 + 3 Combine like terms: -3.464101615 + 3 = -0.464101615 x = -0.464101615 Simplifying x = -0.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.464101615, -0.464101615}Solution
x = {6.464101615, -0.464101615}
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