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Simplifying 0 = 2x2 + 24x + -8 Reorder the terms: 0 = -8 + 24x + 2x2 Solving 0 = -8 + 24x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 8 = 8 8 + -24x + -2x2 = -8 + 24x + 2x2 + 8 + -24x + -2x2 Reorder the terms: 8 + -24x + -2x2 = -8 + 8 + 24x + -24x + 2x2 + -2x2 Combine like terms: -8 + 8 = 0 8 + -24x + -2x2 = 0 + 24x + -24x + 2x2 + -2x2 8 + -24x + -2x2 = 24x + -24x + 2x2 + -2x2 Combine like terms: 24x + -24x = 0 8 + -24x + -2x2 = 0 + 2x2 + -2x2 8 + -24x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 8 + -24x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -12x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -12x + -1x2)' equal to zero and attempt to solve: Simplifying 4 + -12x + -1x2 = 0 Solving 4 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + 12x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 12x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 12x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 12x + x2 = 0 + 4 12x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 12x + x2 = 4 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 = 4 + 36 Reorder the terms: 36 + 12x + x2 = 4 + 36 Combine like terms: 4 + 36 = 40 36 + 12x + x2 = 40 Factor a perfect square on the left side: (x + 6)(x + 6) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + 6) equal to 6.32455532 and -6.32455532.Subproblem 1
x + 6 = 6.32455532 Simplifying x + 6 = 6.32455532 Reorder the terms: 6 + x = 6.32455532 Solving 6 + x = 6.32455532 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 = 6.32455532 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.32455532 + -6 x = 6.32455532 + -6 Combine like terms: 6.32455532 + -6 = 0.32455532 x = 0.32455532 Simplifying x = 0.32455532Subproblem 2
x + 6 = -6.32455532 Simplifying x + 6 = -6.32455532 Reorder the terms: 6 + x = -6.32455532 Solving 6 + x = -6.32455532 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 = -6.32455532 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.32455532 + -6 x = -6.32455532 + -6 Combine like terms: -6.32455532 + -6 = -12.32455532 x = -12.32455532 Simplifying x = -12.32455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.32455532, -12.32455532}Solution
x = {0.32455532, -12.32455532}
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