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Simplifying -16x3 + -15x2 + 16x = 0 Reorder the terms: 16x + -15x2 + -16x3 = 0 Solving 16x + -15x2 + -16x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(16 + -15x + -16x2) = 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 '(16 + -15x + -16x2)' equal to zero and attempt to solve: Simplifying 16 + -15x + -16x2 = 0 Solving 16 + -15x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -1 + 0.9375x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.9375x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.9375x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.9375x + x2 = 0 + 1 0.9375x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.9375x + x2 = 1 The x term is 0.9375x. Take half its coefficient (0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. 0.9375x + 0.2197265625 + x2 = 1 + 0.2197265625 Reorder the terms: 0.2197265625 + 0.9375x + x2 = 1 + 0.2197265625 Combine like terms: 1 + 0.2197265625 = 1.2197265625 0.2197265625 + 0.9375x + x2 = 1.2197265625 Factor a perfect square on the left side: (x + 0.46875)(x + 0.46875) = 1.2197265625 Calculate the square root of the right side: 1.104412315 Break this problem into two subproblems by setting (x + 0.46875) equal to 1.104412315 and -1.104412315.Subproblem 1
x + 0.46875 = 1.104412315 Simplifying x + 0.46875 = 1.104412315 Reorder the terms: 0.46875 + x = 1.104412315 Solving 0.46875 + x = 1.104412315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.46875' to each side of the equation. 0.46875 + -0.46875 + x = 1.104412315 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + x = 1.104412315 + -0.46875 x = 1.104412315 + -0.46875 Combine like terms: 1.104412315 + -0.46875 = 0.635662315 x = 0.635662315 Simplifying x = 0.635662315Subproblem 2
x + 0.46875 = -1.104412315 Simplifying x + 0.46875 = -1.104412315 Reorder the terms: 0.46875 + x = -1.104412315 Solving 0.46875 + x = -1.104412315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.46875' to each side of the equation. 0.46875 + -0.46875 + x = -1.104412315 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + x = -1.104412315 + -0.46875 x = -1.104412315 + -0.46875 Combine like terms: -1.104412315 + -0.46875 = -1.573162315 x = -1.573162315 Simplifying x = -1.573162315Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.635662315, -1.573162315}Solution
x = {0, 0.635662315, -1.573162315}
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