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Simplifying 8x3 + 44x2 + 24x = 0 Reorder the terms: 24x + 44x2 + 8x3 = 0 Solving 24x + 44x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(6 + 11x + 2x2) = 0 Ignore the factor 4.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 '(6 + 11x + 2x2)' equal to zero and attempt to solve: Simplifying 6 + 11x + 2x2 = 0 Solving 6 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + 5.5x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 5.5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 5.5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5.5x + x2 = 0 + -3 5.5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 5.5x + x2 = -3 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = -3 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = -3 + 7.5625 Combine like terms: -3 + 7.5625 = 4.5625 7.5625 + 5.5x + x2 = 4.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (x + 2.75) equal to 2.136000936 and -2.136000936.Subproblem 1
x + 2.75 = 2.136000936 Simplifying x + 2.75 = 2.136000936 Reorder the terms: 2.75 + x = 2.136000936 Solving 2.75 + x = 2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 2.136000936 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 2.136000936 + -2.75 x = 2.136000936 + -2.75 Combine like terms: 2.136000936 + -2.75 = -0.613999064 x = -0.613999064 Simplifying x = -0.613999064Subproblem 2
x + 2.75 = -2.136000936 Simplifying x + 2.75 = -2.136000936 Reorder the terms: 2.75 + x = -2.136000936 Solving 2.75 + x = -2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -2.136000936 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -2.136000936 + -2.75 x = -2.136000936 + -2.75 Combine like terms: -2.136000936 + -2.75 = -4.886000936 x = -4.886000936 Simplifying x = -4.886000936Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.613999064, -4.886000936}Solution
x = {0, -0.613999064, -4.886000936}
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