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Simplifying 2x(2x2 + 24x + 27) = 0 Reorder the terms: 2x(27 + 24x + 2x2) = 0 (27 * 2x + 24x * 2x + 2x2 * 2x) = 0 (54x + 48x2 + 4x3) = 0 Solving 54x + 48x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(27 + 24x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(27 + 24x + 2x2)' equal to zero and attempt to solve: Simplifying 27 + 24x + 2x2 = 0 Solving 27 + 24x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13.5 + 12x + x2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + 12x + -13.5 + x2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + 12x + x2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + 12x + x2 = 0 + -13.5 12x + x2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 12x + x2 = -13.5 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 = -13.5 + 36 Reorder the terms: 36 + 12x + x2 = -13.5 + 36 Combine like terms: -13.5 + 36 = 22.5 36 + 12x + x2 = 22.5 Factor a perfect square on the left side: (x + 6)(x + 6) = 22.5 Calculate the square root of the right side: 4.74341649 Break this problem into two subproblems by setting (x + 6) equal to 4.74341649 and -4.74341649.Subproblem 1
x + 6 = 4.74341649 Simplifying x + 6 = 4.74341649 Reorder the terms: 6 + x = 4.74341649 Solving 6 + x = 4.74341649 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 = 4.74341649 + -6 Combine like terms: 6 + -6 = 0 0 + x = 4.74341649 + -6 x = 4.74341649 + -6 Combine like terms: 4.74341649 + -6 = -1.25658351 x = -1.25658351 Simplifying x = -1.25658351Subproblem 2
x + 6 = -4.74341649 Simplifying x + 6 = -4.74341649 Reorder the terms: 6 + x = -4.74341649 Solving 6 + x = -4.74341649 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 = -4.74341649 + -6 Combine like terms: 6 + -6 = 0 0 + x = -4.74341649 + -6 x = -4.74341649 + -6 Combine like terms: -4.74341649 + -6 = -10.74341649 x = -10.74341649 Simplifying x = -10.74341649Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.25658351, -10.74341649}Solution
x = {0, -1.25658351, -10.74341649}
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