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Simplifying 15x3 + x2 + 2x = 0 Reorder the terms: 2x + x2 + 15x3 = 0 Solving 2x + x2 + 15x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(2 + x + 15x2) = 0Subproblem 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 '(2 + x + 15x2)' equal to zero and attempt to solve: Simplifying 2 + x + 15x2 = 0 Solving 2 + x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.1333333333 + 0.06666666667x + x2 = 0 Move the constant term to the right: Add '-0.1333333333' to each side of the equation. 0.1333333333 + 0.06666666667x + -0.1333333333 + x2 = 0 + -0.1333333333 Reorder the terms: 0.1333333333 + -0.1333333333 + 0.06666666667x + x2 = 0 + -0.1333333333 Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000 0.0000000000 + 0.06666666667x + x2 = 0 + -0.1333333333 0.06666666667x + x2 = 0 + -0.1333333333 Combine like terms: 0 + -0.1333333333 = -0.1333333333 0.06666666667x + x2 = -0.1333333333 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. 0.06666666667x + 0.25 + x2 = -0.1333333333 + 0.25 Reorder the terms: 0.25 + 0.06666666667x + x2 = -0.1333333333 + 0.25 Combine like terms: -0.1333333333 + 0.25 = 0.1166666667 0.25 + 0.06666666667x + x2 = 0.1166666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.1166666667 Calculate the square root of the right side: 0.341565026 Break this problem into two subproblems by setting (x + 0.5) equal to 0.341565026 and -0.341565026.Subproblem 1
x + 0.5 = 0.341565026 Simplifying x + 0.5 = 0.341565026 Reorder the terms: 0.5 + x = 0.341565026 Solving 0.5 + x = 0.341565026 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 = 0.341565026 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.341565026 + -0.5 x = 0.341565026 + -0.5 Combine like terms: 0.341565026 + -0.5 = -0.158434974 x = -0.158434974 Simplifying x = -0.158434974Subproblem 2
x + 0.5 = -0.341565026 Simplifying x + 0.5 = -0.341565026 Reorder the terms: 0.5 + x = -0.341565026 Solving 0.5 + x = -0.341565026 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 = -0.341565026 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.341565026 + -0.5 x = -0.341565026 + -0.5 Combine like terms: -0.341565026 + -0.5 = -0.841565026 x = -0.841565026 Simplifying x = -0.841565026Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.158434974, -0.841565026}Solution
x = {0, -0.158434974, -0.841565026}
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