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Simplifying -13x3 + 130x2 + -200x = 0 Reorder the terms: -200x + 130x2 + -13x3 = 0 Solving -200x + 130x2 + -13x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-200 + 130x + -13x2) = 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 '(-200 + 130x + -13x2)' equal to zero and attempt to solve: Simplifying -200 + 130x + -13x2 = 0 Solving -200 + 130x + -13x2 = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. 15.38461538 + -10x + x2 = 0 Move the constant term to the right: Add '-15.38461538' to each side of the equation. 15.38461538 + -10x + -15.38461538 + x2 = 0 + -15.38461538 Reorder the terms: 15.38461538 + -15.38461538 + -10x + x2 = 0 + -15.38461538 Combine like terms: 15.38461538 + -15.38461538 = 0.00000000 0.00000000 + -10x + x2 = 0 + -15.38461538 -10x + x2 = 0 + -15.38461538 Combine like terms: 0 + -15.38461538 = -15.38461538 -10x + x2 = -15.38461538 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -15.38461538 + 25 Reorder the terms: 25 + -10x + x2 = -15.38461538 + 25 Combine like terms: -15.38461538 + 25 = 9.61538462 25 + -10x + x2 = 9.61538462 Factor a perfect square on the left side: (x + -5)(x + -5) = 9.61538462 Calculate the square root of the right side: 3.100868365 Break this problem into two subproblems by setting (x + -5) equal to 3.100868365 and -3.100868365.Subproblem 1
x + -5 = 3.100868365 Simplifying x + -5 = 3.100868365 Reorder the terms: -5 + x = 3.100868365 Solving -5 + x = 3.100868365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.100868365 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.100868365 + 5 x = 3.100868365 + 5 Combine like terms: 3.100868365 + 5 = 8.100868365 x = 8.100868365 Simplifying x = 8.100868365Subproblem 2
x + -5 = -3.100868365 Simplifying x + -5 = -3.100868365 Reorder the terms: -5 + x = -3.100868365 Solving -5 + x = -3.100868365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.100868365 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.100868365 + 5 x = -3.100868365 + 5 Combine like terms: -3.100868365 + 5 = 1.899131635 x = 1.899131635 Simplifying x = 1.899131635Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.100868365, 1.899131635}Solution
x = {0, 8.100868365, 1.899131635}
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