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Simplifying 8x3 + -15x2 + 4x = 0 Reorder the terms: 4x + -15x2 + 8x3 = 0 Solving 4x + -15x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(4 + -15x + 8x2) = 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 '(4 + -15x + 8x2)' equal to zero and attempt to solve: Simplifying 4 + -15x + 8x2 = 0 Solving 4 + -15x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.5 + -1.875x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.875x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.875x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.875x + x2 = 0 + -0.5 -1.875x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1.875x + x2 = -0.5 The x term is -1.875x. Take half its coefficient (-0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. -1.875x + 0.87890625 + x2 = -0.5 + 0.87890625 Reorder the terms: 0.87890625 + -1.875x + x2 = -0.5 + 0.87890625 Combine like terms: -0.5 + 0.87890625 = 0.37890625 0.87890625 + -1.875x + x2 = 0.37890625 Factor a perfect square on the left side: (x + -0.9375)(x + -0.9375) = 0.37890625 Calculate the square root of the right side: 0.615553613 Break this problem into two subproblems by setting (x + -0.9375) equal to 0.615553613 and -0.615553613.Subproblem 1
x + -0.9375 = 0.615553613 Simplifying x + -0.9375 = 0.615553613 Reorder the terms: -0.9375 + x = 0.615553613 Solving -0.9375 + x = 0.615553613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = 0.615553613 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = 0.615553613 + 0.9375 x = 0.615553613 + 0.9375 Combine like terms: 0.615553613 + 0.9375 = 1.553053613 x = 1.553053613 Simplifying x = 1.553053613Subproblem 2
x + -0.9375 = -0.615553613 Simplifying x + -0.9375 = -0.615553613 Reorder the terms: -0.9375 + x = -0.615553613 Solving -0.9375 + x = -0.615553613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = -0.615553613 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = -0.615553613 + 0.9375 x = -0.615553613 + 0.9375 Combine like terms: -0.615553613 + 0.9375 = 0.321946387 x = 0.321946387 Simplifying x = 0.321946387Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.553053613, 0.321946387}Solution
x = {0, 1.553053613, 0.321946387}
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