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Simplifying x3 + -1x3 + -15x2 + 3x + 36 = 0 Reorder the terms: 36 + 3x + -15x2 + x3 + -1x3 = 0 Combine like terms: x3 + -1x3 = 0 36 + 3x + -15x2 + 0 = 0 36 + 3x + -15x2 = 0 Solving 36 + 3x + -15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(12 + x + -5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(12 + x + -5x2)' equal to zero and attempt to solve: Simplifying 12 + x + -5x2 = 0 Solving 12 + x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.4 + -0.2x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -0.2x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -0.2x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -0.2x + x2 = 0 + 2.4 -0.2x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -0.2x + x2 = 2.4 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.2x + 0.25 + x2 = 2.4 + 0.25 Reorder the terms: 0.25 + -0.2x + x2 = 2.4 + 0.25 Combine like terms: 2.4 + 0.25 = 2.65 0.25 + -0.2x + x2 = 2.65 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.65 Calculate the square root of the right side: 1.62788206 Break this problem into two subproblems by setting (x + 0.5) equal to 1.62788206 and -1.62788206.Subproblem 1
x + 0.5 = 1.62788206 Simplifying x + 0.5 = 1.62788206 Reorder the terms: 0.5 + x = 1.62788206 Solving 0.5 + x = 1.62788206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.62788206 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.62788206 + -0.5 x = 1.62788206 + -0.5 Combine like terms: 1.62788206 + -0.5 = 1.12788206 x = 1.12788206 Simplifying x = 1.12788206Subproblem 2
x + 0.5 = -1.62788206 Simplifying x + 0.5 = -1.62788206 Reorder the terms: 0.5 + x = -1.62788206 Solving 0.5 + x = -1.62788206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.62788206 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.62788206 + -0.5 x = -1.62788206 + -0.5 Combine like terms: -1.62788206 + -0.5 = -2.12788206 x = -2.12788206 Simplifying x = -2.12788206Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.12788206, -2.12788206}Solution
x = {1.12788206, -2.12788206}
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