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Simplifying -2x2 + -24x + 24 = 0 Reorder the terms: 24 + -24x + -2x2 = 0 Solving 24 + -24x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -12x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + -12x + -1x2)' equal to zero and attempt to solve: Simplifying 12 + -12x + -1x2 = 0 Solving 12 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + 12x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 12x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 12x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 12x + x2 = 0 + 12 12x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 12x + x2 = 12 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 12 + 36 Reorder the terms: 36 + 12x + x2 = 12 + 36 Combine like terms: 12 + 36 = 48 36 + 12x + x2 = 48 Factor a perfect square on the left side: (x + 6)(x + 6) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + 6) equal to 6.92820323 and -6.92820323.Subproblem 1
x + 6 = 6.92820323 Simplifying x + 6 = 6.92820323 Reorder the terms: 6 + x = 6.92820323 Solving 6 + x = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 6.92820323 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.92820323 + -6 x = 6.92820323 + -6 Combine like terms: 6.92820323 + -6 = 0.92820323 x = 0.92820323 Simplifying x = 0.92820323Subproblem 2
x + 6 = -6.92820323 Simplifying x + 6 = -6.92820323 Reorder the terms: 6 + x = -6.92820323 Solving 6 + x = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -6.92820323 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.92820323 + -6 x = -6.92820323 + -6 Combine like terms: -6.92820323 + -6 = -12.92820323 x = -12.92820323 Simplifying x = -12.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.92820323, -12.92820323}Solution
x = {0.92820323, -12.92820323}
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