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Simplifying -2x2 + 12x + 24 = 0 Reorder the terms: 24 + 12x + -2x2 = 0 Solving 24 + 12x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 6x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying 12 + 6x + -1x2 = 0 Solving 12 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + -6x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -6x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -6x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -6x + x2 = 0 + 12 -6x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -6x + x2 = 12 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 = 12 + 9 Reorder the terms: 9 + -6x + x2 = 12 + 9 Combine like terms: 12 + 9 = 21 9 + -6x + x2 = 21 Factor a perfect square on the left side: (x + -3)(x + -3) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + -3) equal to 4.582575695 and -4.582575695.Subproblem 1
x + -3 = 4.582575695 Simplifying x + -3 = 4.582575695 Reorder the terms: -3 + x = 4.582575695 Solving -3 + x = 4.582575695 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 = 4.582575695 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.582575695 + 3 x = 4.582575695 + 3 Combine like terms: 4.582575695 + 3 = 7.582575695 x = 7.582575695 Simplifying x = 7.582575695Subproblem 2
x + -3 = -4.582575695 Simplifying x + -3 = -4.582575695 Reorder the terms: -3 + x = -4.582575695 Solving -3 + x = -4.582575695 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 = -4.582575695 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.582575695 + 3 x = -4.582575695 + 3 Combine like terms: -4.582575695 + 3 = -1.582575695 x = -1.582575695 Simplifying x = -1.582575695Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.582575695, -1.582575695}Solution
x = {7.582575695, -1.582575695}
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