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Simplifying 20x3 + 68x2 + 40x = 0 Reorder the terms: 40x + 68x2 + 20x3 = 0 Solving 40x + 68x2 + 20x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(10 + 17x + 5x2) = 0 Ignore the factor 4.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 '(10 + 17x + 5x2)' equal to zero and attempt to solve: Simplifying 10 + 17x + 5x2 = 0 Solving 10 + 17x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + 3.4x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 3.4x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 3.4x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3.4x + x2 = 0 + -2 3.4x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 3.4x + x2 = -2 The x term is 3.4x. Take half its coefficient (1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. 3.4x + 2.89 + x2 = -2 + 2.89 Reorder the terms: 2.89 + 3.4x + x2 = -2 + 2.89 Combine like terms: -2 + 2.89 = 0.89 2.89 + 3.4x + x2 = 0.89 Factor a perfect square on the left side: (x + 1.7)(x + 1.7) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (x + 1.7) equal to 0.943398113 and -0.943398113.Subproblem 1
x + 1.7 = 0.943398113 Simplifying x + 1.7 = 0.943398113 Reorder the terms: 1.7 + x = 0.943398113 Solving 1.7 + x = 0.943398113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = 0.943398113 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = 0.943398113 + -1.7 x = 0.943398113 + -1.7 Combine like terms: 0.943398113 + -1.7 = -0.756601887 x = -0.756601887 Simplifying x = -0.756601887Subproblem 2
x + 1.7 = -0.943398113 Simplifying x + 1.7 = -0.943398113 Reorder the terms: 1.7 + x = -0.943398113 Solving 1.7 + x = -0.943398113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = -0.943398113 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = -0.943398113 + -1.7 x = -0.943398113 + -1.7 Combine like terms: -0.943398113 + -1.7 = -2.643398113 x = -2.643398113 Simplifying x = -2.643398113Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.756601887, -2.643398113}Solution
x = {0, -0.756601887, -2.643398113}
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