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Simplifying 3x3 = 27x2 + 66x + -3x3 Reorder the terms: 3x3 = 66x + 27x2 + -3x3 Solving 3x3 = 66x + 27x2 + -3x3 Solving for variable 'x'. Reorder the terms: -66x + -27x2 + 3x3 + 3x3 = 66x + 27x2 + -3x3 + -66x + -27x2 + 3x3 Combine like terms: 3x3 + 3x3 = 6x3 -66x + -27x2 + 6x3 = 66x + 27x2 + -3x3 + -66x + -27x2 + 3x3 Reorder the terms: -66x + -27x2 + 6x3 = 66x + -66x + 27x2 + -27x2 + -3x3 + 3x3 Combine like terms: 66x + -66x = 0 -66x + -27x2 + 6x3 = 0 + 27x2 + -27x2 + -3x3 + 3x3 -66x + -27x2 + 6x3 = 27x2 + -27x2 + -3x3 + 3x3 Combine like terms: 27x2 + -27x2 = 0 -66x + -27x2 + 6x3 = 0 + -3x3 + 3x3 -66x + -27x2 + 6x3 = -3x3 + 3x3 Combine like terms: -3x3 + 3x3 = 0 -66x + -27x2 + 6x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-22 + -9x + 2x2) = 0 Ignore the factor 3.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 '(-22 + -9x + 2x2)' equal to zero and attempt to solve: Simplifying -22 + -9x + 2x2 = 0 Solving -22 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11 + -4.5x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -4.5x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -4.5x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -4.5x + x2 = 0 + 11 -4.5x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -4.5x + x2 = 11 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 11 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 11 + 5.0625 Combine like terms: 11 + 5.0625 = 16.0625 5.0625 + -4.5x + x2 = 16.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 16.0625 Calculate the square root of the right side: 4.007804885 Break this problem into two subproblems by setting (x + -2.25) equal to 4.007804885 and -4.007804885.Subproblem 1
x + -2.25 = 4.007804885 Simplifying x + -2.25 = 4.007804885 Reorder the terms: -2.25 + x = 4.007804885 Solving -2.25 + x = 4.007804885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 4.007804885 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 4.007804885 + 2.25 x = 4.007804885 + 2.25 Combine like terms: 4.007804885 + 2.25 = 6.257804885 x = 6.257804885 Simplifying x = 6.257804885Subproblem 2
x + -2.25 = -4.007804885 Simplifying x + -2.25 = -4.007804885 Reorder the terms: -2.25 + x = -4.007804885 Solving -2.25 + x = -4.007804885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -4.007804885 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -4.007804885 + 2.25 x = -4.007804885 + 2.25 Combine like terms: -4.007804885 + 2.25 = -1.757804885 x = -1.757804885 Simplifying x = -1.757804885Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.257804885, -1.757804885}Solution
x = {0, 6.257804885, -1.757804885}
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