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Simplifying 20x3 + 33x2 = 7x Reorder the terms: 33x2 + 20x3 = 7x Solving 33x2 + 20x3 = 7x Solving for variable 'x'. Reorder the terms: -7x + 33x2 + 20x3 = 7x + -7x Combine like terms: 7x + -7x = 0 -7x + 33x2 + 20x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-7 + 33x + 20x2) = 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 '(-7 + 33x + 20x2)' equal to zero and attempt to solve: Simplifying -7 + 33x + 20x2 = 0 Solving -7 + 33x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.35 + 1.65x + x2 = 0 Move the constant term to the right: Add '0.35' to each side of the equation. -0.35 + 1.65x + 0.35 + x2 = 0 + 0.35 Reorder the terms: -0.35 + 0.35 + 1.65x + x2 = 0 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + 1.65x + x2 = 0 + 0.35 1.65x + x2 = 0 + 0.35 Combine like terms: 0 + 0.35 = 0.35 1.65x + x2 = 0.35 The x term is 1.65x. Take half its coefficient (0.825). Square it (0.680625) and add it to both sides. Add '0.680625' to each side of the equation. 1.65x + 0.680625 + x2 = 0.35 + 0.680625 Reorder the terms: 0.680625 + 1.65x + x2 = 0.35 + 0.680625 Combine like terms: 0.35 + 0.680625 = 1.030625 0.680625 + 1.65x + x2 = 1.030625 Factor a perfect square on the left side: (x + 0.825)(x + 0.825) = 1.030625 Calculate the square root of the right side: 1.015197025 Break this problem into two subproblems by setting (x + 0.825) equal to 1.015197025 and -1.015197025.Subproblem 1
x + 0.825 = 1.015197025 Simplifying x + 0.825 = 1.015197025 Reorder the terms: 0.825 + x = 1.015197025 Solving 0.825 + x = 1.015197025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.825' to each side of the equation. 0.825 + -0.825 + x = 1.015197025 + -0.825 Combine like terms: 0.825 + -0.825 = 0.000 0.000 + x = 1.015197025 + -0.825 x = 1.015197025 + -0.825 Combine like terms: 1.015197025 + -0.825 = 0.190197025 x = 0.190197025 Simplifying x = 0.190197025Subproblem 2
x + 0.825 = -1.015197025 Simplifying x + 0.825 = -1.015197025 Reorder the terms: 0.825 + x = -1.015197025 Solving 0.825 + x = -1.015197025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.825' to each side of the equation. 0.825 + -0.825 + x = -1.015197025 + -0.825 Combine like terms: 0.825 + -0.825 = 0.000 0.000 + x = -1.015197025 + -0.825 x = -1.015197025 + -0.825 Combine like terms: -1.015197025 + -0.825 = -1.840197025 x = -1.840197025 Simplifying x = -1.840197025Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.190197025, -1.840197025}Solution
x = {0, 0.190197025, -1.840197025}
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