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Simplifying 0 = 280x + 8960 + -13x2 Reorder the terms: 0 = 8960 + 280x + -13x2 Solving 0 = 8960 + 280x + -13x2 Solving for variable 'x'. Combine like terms: 0 + -8960 = -8960 -8960 + -280x + 13x2 = 8960 + 280x + -13x2 + -8960 + -280x + 13x2 Reorder the terms: -8960 + -280x + 13x2 = 8960 + -8960 + 280x + -280x + -13x2 + 13x2 Combine like terms: 8960 + -8960 = 0 -8960 + -280x + 13x2 = 0 + 280x + -280x + -13x2 + 13x2 -8960 + -280x + 13x2 = 280x + -280x + -13x2 + 13x2 Combine like terms: 280x + -280x = 0 -8960 + -280x + 13x2 = 0 + -13x2 + 13x2 -8960 + -280x + 13x2 = -13x2 + 13x2 Combine like terms: -13x2 + 13x2 = 0 -8960 + -280x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -689.2307692 + -21.53846154x + x2 = 0 Move the constant term to the right: Add '689.2307692' to each side of the equation. -689.2307692 + -21.53846154x + 689.2307692 + x2 = 0 + 689.2307692 Reorder the terms: -689.2307692 + 689.2307692 + -21.53846154x + x2 = 0 + 689.2307692 Combine like terms: -689.2307692 + 689.2307692 = 0.0000000 0.0000000 + -21.53846154x + x2 = 0 + 689.2307692 -21.53846154x + x2 = 0 + 689.2307692 Combine like terms: 0 + 689.2307692 = 689.2307692 -21.53846154x + x2 = 689.2307692 The x term is -21.53846154x. Take half its coefficient (-10.76923077). Square it (115.9763314) and add it to both sides. Add '115.9763314' to each side of the equation. -21.53846154x + 115.9763314 + x2 = 689.2307692 + 115.9763314 Reorder the terms: 115.9763314 + -21.53846154x + x2 = 689.2307692 + 115.9763314 Combine like terms: 689.2307692 + 115.9763314 = 805.2071006 115.9763314 + -21.53846154x + x2 = 805.2071006 Factor a perfect square on the left side: (x + -10.76923077)(x + -10.76923077) = 805.2071006 Calculate the square root of the right side: 28.376171352 Break this problem into two subproblems by setting (x + -10.76923077) equal to 28.376171352 and -28.376171352.Subproblem 1
x + -10.76923077 = 28.376171352 Simplifying x + -10.76923077 = 28.376171352 Reorder the terms: -10.76923077 + x = 28.376171352 Solving -10.76923077 + x = 28.376171352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.76923077' to each side of the equation. -10.76923077 + 10.76923077 + x = 28.376171352 + 10.76923077 Combine like terms: -10.76923077 + 10.76923077 = 0.00000000 0.00000000 + x = 28.376171352 + 10.76923077 x = 28.376171352 + 10.76923077 Combine like terms: 28.376171352 + 10.76923077 = 39.145402122 x = 39.145402122 Simplifying x = 39.145402122Subproblem 2
x + -10.76923077 = -28.376171352 Simplifying x + -10.76923077 = -28.376171352 Reorder the terms: -10.76923077 + x = -28.376171352 Solving -10.76923077 + x = -28.376171352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.76923077' to each side of the equation. -10.76923077 + 10.76923077 + x = -28.376171352 + 10.76923077 Combine like terms: -10.76923077 + 10.76923077 = 0.00000000 0.00000000 + x = -28.376171352 + 10.76923077 x = -28.376171352 + 10.76923077 Combine like terms: -28.376171352 + 10.76923077 = -17.606940582 x = -17.606940582 Simplifying x = -17.606940582Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.145402122, -17.606940582}
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