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Simplifying 16x3 + -9x2 + -10x = 0 Reorder the terms: -10x + -9x2 + 16x3 = 0 Solving -10x + -9x2 + 16x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-10 + -9x + 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 '(-10 + -9x + 16x2)' equal to zero and attempt to solve: Simplifying -10 + -9x + 16x2 = 0 Solving -10 + -9x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.625 + -0.5625x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -0.5625x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -0.5625x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -0.5625x + x2 = 0 + 0.625 -0.5625x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -0.5625x + x2 = 0.625 The x term is -0.5625x. Take half its coefficient (-0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. -0.5625x + 0.0791015625 + x2 = 0.625 + 0.0791015625 Reorder the terms: 0.0791015625 + -0.5625x + x2 = 0.625 + 0.0791015625 Combine like terms: 0.625 + 0.0791015625 = 0.7041015625 0.0791015625 + -0.5625x + x2 = 0.7041015625 Factor a perfect square on the left side: (x + -0.28125)(x + -0.28125) = 0.7041015625 Calculate the square root of the right side: 0.839107599 Break this problem into two subproblems by setting (x + -0.28125) equal to 0.839107599 and -0.839107599.Subproblem 1
x + -0.28125 = 0.839107599 Simplifying x + -0.28125 = 0.839107599 Reorder the terms: -0.28125 + x = 0.839107599 Solving -0.28125 + x = 0.839107599 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + x = 0.839107599 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x = 0.839107599 + 0.28125 x = 0.839107599 + 0.28125 Combine like terms: 0.839107599 + 0.28125 = 1.120357599 x = 1.120357599 Simplifying x = 1.120357599Subproblem 2
x + -0.28125 = -0.839107599 Simplifying x + -0.28125 = -0.839107599 Reorder the terms: -0.28125 + x = -0.839107599 Solving -0.28125 + x = -0.839107599 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + x = -0.839107599 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x = -0.839107599 + 0.28125 x = -0.839107599 + 0.28125 Combine like terms: -0.839107599 + 0.28125 = -0.557857599 x = -0.557857599 Simplifying x = -0.557857599Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.120357599, -0.557857599}Solution
x = {0, 1.120357599, -0.557857599}
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