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Simplifying 0 = x2 + -13x + 24 Reorder the terms: 0 = 24 + -13x + x2 Solving 0 = 24 + -13x + x2 Solving for variable 'x'. Combine like terms: 0 + -24 = -24 -24 + 13x + -1x2 = 24 + -13x + x2 + -24 + 13x + -1x2 Reorder the terms: -24 + 13x + -1x2 = 24 + -24 + -13x + 13x + x2 + -1x2 Combine like terms: 24 + -24 = 0 -24 + 13x + -1x2 = 0 + -13x + 13x + x2 + -1x2 -24 + 13x + -1x2 = -13x + 13x + x2 + -1x2 Combine like terms: -13x + 13x = 0 -24 + 13x + -1x2 = 0 + x2 + -1x2 -24 + 13x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -24 + 13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 24 + -13x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -13x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -13x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -13x + x2 = 0 + -24 -13x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -13x + x2 = -24 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -24 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -24 + 42.25 Combine like terms: -24 + 42.25 = 18.25 42.25 + -13x + x2 = 18.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + -6.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x + -6.5 = 4.272001873 Simplifying x + -6.5 = 4.272001873 Reorder the terms: -6.5 + x = 4.272001873 Solving -6.5 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 4.272001873 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 4.272001873 + 6.5 x = 4.272001873 + 6.5 Combine like terms: 4.272001873 + 6.5 = 10.772001873 x = 10.772001873 Simplifying x = 10.772001873Subproblem 2
x + -6.5 = -4.272001873 Simplifying x + -6.5 = -4.272001873 Reorder the terms: -6.5 + x = -4.272001873 Solving -6.5 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -4.272001873 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -4.272001873 + 6.5 x = -4.272001873 + 6.5 Combine like terms: -4.272001873 + 6.5 = 2.227998127 x = 2.227998127 Simplifying x = 2.227998127Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.772001873, 2.227998127}
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