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Simplifying -56x3 + 42x2 + 21x = 0 Reorder the terms: 21x + 42x2 + -56x3 = 0 Solving 21x + 42x2 + -56x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7x'. 7x(3 + 6x + -8x2) = 0 Ignore the factor 7.Subproblem 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 '(3 + 6x + -8x2)' equal to zero and attempt to solve: Simplifying 3 + 6x + -8x2 = 0 Solving 3 + 6x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + -0.75x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -0.75x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -0.75x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -0.75x + x2 = 0 + 0.375 -0.75x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -0.75x + x2 = 0.375 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 0.375 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 0.375 + 0.140625 Combine like terms: 0.375 + 0.140625 = 0.515625 0.140625 + -0.75x + x2 = 0.515625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (x + -0.375) equal to 0.718070331 and -0.718070331.Subproblem 1
x + -0.375 = 0.718070331 Simplifying x + -0.375 = 0.718070331 Reorder the terms: -0.375 + x = 0.718070331 Solving -0.375 + x = 0.718070331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 0.718070331 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 0.718070331 + 0.375 x = 0.718070331 + 0.375 Combine like terms: 0.718070331 + 0.375 = 1.093070331 x = 1.093070331 Simplifying x = 1.093070331Subproblem 2
x + -0.375 = -0.718070331 Simplifying x + -0.375 = -0.718070331 Reorder the terms: -0.375 + x = -0.718070331 Solving -0.375 + x = -0.718070331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -0.718070331 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -0.718070331 + 0.375 x = -0.718070331 + 0.375 Combine like terms: -0.718070331 + 0.375 = -0.343070331 x = -0.343070331 Simplifying x = -0.343070331Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.093070331, -0.343070331}Solution
x = {0, 1.093070331, -0.343070331}
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