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Simplifying 2x3 + 18x2 + 14x = 0 Reorder the terms: 14x + 18x2 + 2x3 = 0 Solving 14x + 18x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(7 + 9x + x2) = 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 '(7 + 9x + x2)' equal to zero and attempt to solve: Simplifying 7 + 9x + x2 = 0 Solving 7 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 9x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 9x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 9x + x2 = 0 + -7 9x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 9x + x2 = -7 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -7 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -7 + 20.25 Combine like terms: -7 + 20.25 = 13.25 20.25 + 9x + x2 = 13.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x + 4.5) equal to 3.640054945 and -3.640054945.Subproblem 1
x + 4.5 = 3.640054945 Simplifying x + 4.5 = 3.640054945 Reorder the terms: 4.5 + x = 3.640054945 Solving 4.5 + x = 3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 3.640054945 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 3.640054945 + -4.5 x = 3.640054945 + -4.5 Combine like terms: 3.640054945 + -4.5 = -0.859945055 x = -0.859945055 Simplifying x = -0.859945055Subproblem 2
x + 4.5 = -3.640054945 Simplifying x + 4.5 = -3.640054945 Reorder the terms: 4.5 + x = -3.640054945 Solving 4.5 + x = -3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -3.640054945 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -3.640054945 + -4.5 x = -3.640054945 + -4.5 Combine like terms: -3.640054945 + -4.5 = -8.140054945 x = -8.140054945 Simplifying x = -8.140054945Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.859945055, -8.140054945}Solution
x = {0, -0.859945055, -8.140054945}
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