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Simplifying 0 = 6x2 + 9x + -24 Reorder the terms: 0 = -24 + 9x + 6x2 Solving 0 = -24 + 9x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 24 = 24 24 + -9x + -6x2 = -24 + 9x + 6x2 + 24 + -9x + -6x2 Reorder the terms: 24 + -9x + -6x2 = -24 + 24 + 9x + -9x + 6x2 + -6x2 Combine like terms: -24 + 24 = 0 24 + -9x + -6x2 = 0 + 9x + -9x + 6x2 + -6x2 24 + -9x + -6x2 = 9x + -9x + 6x2 + -6x2 Combine like terms: 9x + -9x = 0 24 + -9x + -6x2 = 0 + 6x2 + -6x2 24 + -9x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 24 + -9x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(8 + -3x + -2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8 + -3x + -2x2)' equal to zero and attempt to solve: Simplifying 8 + -3x + -2x2 = 0 Solving 8 + -3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4 + 1.5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 1.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 1.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 1.5x + x2 = 0 + 4 1.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 1.5x + x2 = 4 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 4 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 4 + 0.5625 Combine like terms: 4 + 0.5625 = 4.5625 0.5625 + 1.5x + x2 = 4.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (x + 0.75) equal to 2.136000936 and -2.136000936.Subproblem 1
x + 0.75 = 2.136000936 Simplifying x + 0.75 = 2.136000936 Reorder the terms: 0.75 + x = 2.136000936 Solving 0.75 + x = 2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.136000936 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.136000936 + -0.75 x = 2.136000936 + -0.75 Combine like terms: 2.136000936 + -0.75 = 1.386000936 x = 1.386000936 Simplifying x = 1.386000936Subproblem 2
x + 0.75 = -2.136000936 Simplifying x + 0.75 = -2.136000936 Reorder the terms: 0.75 + x = -2.136000936 Solving 0.75 + x = -2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.136000936 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.136000936 + -0.75 x = -2.136000936 + -0.75 Combine like terms: -2.136000936 + -0.75 = -2.886000936 x = -2.886000936 Simplifying x = -2.886000936Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.386000936, -2.886000936}Solution
x = {1.386000936, -2.886000936}
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