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Simplifying 13x2 + -241x + -432 = 0 Reorder the terms: -432 + -241x + 13x2 = 0 Solving -432 + -241x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -33.23076923 + -18.53846154x + x2 = 0 Move the constant term to the right: Add '33.23076923' to each side of the equation. -33.23076923 + -18.53846154x + 33.23076923 + x2 = 0 + 33.23076923 Reorder the terms: -33.23076923 + 33.23076923 + -18.53846154x + x2 = 0 + 33.23076923 Combine like terms: -33.23076923 + 33.23076923 = 0.00000000 0.00000000 + -18.53846154x + x2 = 0 + 33.23076923 -18.53846154x + x2 = 0 + 33.23076923 Combine like terms: 0 + 33.23076923 = 33.23076923 -18.53846154x + x2 = 33.23076923 The x term is -18.53846154x. Take half its coefficient (-9.26923077). Square it (85.91863907) and add it to both sides. Add '85.91863907' to each side of the equation. -18.53846154x + 85.91863907 + x2 = 33.23076923 + 85.91863907 Reorder the terms: 85.91863907 + -18.53846154x + x2 = 33.23076923 + 85.91863907 Combine like terms: 33.23076923 + 85.91863907 = 119.1494083 85.91863907 + -18.53846154x + x2 = 119.1494083 Factor a perfect square on the left side: (x + -9.26923077)(x + -9.26923077) = 119.1494083 Calculate the square root of the right side: 10.915558085 Break this problem into two subproblems by setting (x + -9.26923077) equal to 10.915558085 and -10.915558085.Subproblem 1
x + -9.26923077 = 10.915558085 Simplifying x + -9.26923077 = 10.915558085 Reorder the terms: -9.26923077 + x = 10.915558085 Solving -9.26923077 + x = 10.915558085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.26923077' to each side of the equation. -9.26923077 + 9.26923077 + x = 10.915558085 + 9.26923077 Combine like terms: -9.26923077 + 9.26923077 = 0.00000000 0.00000000 + x = 10.915558085 + 9.26923077 x = 10.915558085 + 9.26923077 Combine like terms: 10.915558085 + 9.26923077 = 20.184788855 x = 20.184788855 Simplifying x = 20.184788855Subproblem 2
x + -9.26923077 = -10.915558085 Simplifying x + -9.26923077 = -10.915558085 Reorder the terms: -9.26923077 + x = -10.915558085 Solving -9.26923077 + x = -10.915558085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.26923077' to each side of the equation. -9.26923077 + 9.26923077 + x = -10.915558085 + 9.26923077 Combine like terms: -9.26923077 + 9.26923077 = 0.00000000 0.00000000 + x = -10.915558085 + 9.26923077 x = -10.915558085 + 9.26923077 Combine like terms: -10.915558085 + 9.26923077 = -1.646327315 x = -1.646327315 Simplifying x = -1.646327315Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.184788855, -1.646327315}
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