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Simplifying -20x3 + -58x2 + -8x = 0 Reorder the terms: -8x + -58x2 + -20x3 = 0 Solving -8x + -58x2 + -20x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2x'. -2x(4 + 29x + 10x2) = 0 Ignore the factor -2.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 '(4 + 29x + 10x2)' equal to zero and attempt to solve: Simplifying 4 + 29x + 10x2 = 0 Solving 4 + 29x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.4 + 2.9x + x2 = 0.0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 2.9x + -0.4 + x2 = 0.0 + -0.4 Reorder the terms: 0.4 + -0.4 + 2.9x + x2 = 0.0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 2.9x + x2 = 0.0 + -0.4 2.9x + x2 = 0.0 + -0.4 Combine like terms: 0.0 + -0.4 = -0.4 2.9x + x2 = -0.4 The x term is 2.9x. Take half its coefficient (1.45). Square it (2.1025) and add it to both sides. Add '2.1025' to each side of the equation. 2.9x + 2.1025 + x2 = -0.4 + 2.1025 Reorder the terms: 2.1025 + 2.9x + x2 = -0.4 + 2.1025 Combine like terms: -0.4 + 2.1025 = 1.7025 2.1025 + 2.9x + x2 = 1.7025 Factor a perfect square on the left side: (x + 1.45)(x + 1.45) = 1.7025 Calculate the square root of the right side: 1.304798835 Break this problem into two subproblems by setting (x + 1.45) equal to 1.304798835 and -1.304798835.Subproblem 1
x + 1.45 = 1.304798835 Simplifying x + 1.45 = 1.304798835 Reorder the terms: 1.45 + x = 1.304798835 Solving 1.45 + x = 1.304798835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.45' to each side of the equation. 1.45 + -1.45 + x = 1.304798835 + -1.45 Combine like terms: 1.45 + -1.45 = 0.00 0.00 + x = 1.304798835 + -1.45 x = 1.304798835 + -1.45 Combine like terms: 1.304798835 + -1.45 = -0.145201165 x = -0.145201165 Simplifying x = -0.145201165Subproblem 2
x + 1.45 = -1.304798835 Simplifying x + 1.45 = -1.304798835 Reorder the terms: 1.45 + x = -1.304798835 Solving 1.45 + x = -1.304798835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.45' to each side of the equation. 1.45 + -1.45 + x = -1.304798835 + -1.45 Combine like terms: 1.45 + -1.45 = 0.00 0.00 + x = -1.304798835 + -1.45 x = -1.304798835 + -1.45 Combine like terms: -1.304798835 + -1.45 = -2.754798835 x = -2.754798835 Simplifying x = -2.754798835Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.145201165, -2.754798835}Solution
x = {0, -0.145201165, -2.754798835}
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