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Simplifying (x + 13)(x + -8) = 5184 Reorder the terms: (13 + x)(x + -8) = 5184 Reorder the terms: (13 + x)(-8 + x) = 5184 Multiply (13 + x) * (-8 + x) (13(-8 + x) + x(-8 + x)) = 5184 ((-8 * 13 + x * 13) + x(-8 + x)) = 5184 ((-104 + 13x) + x(-8 + x)) = 5184 (-104 + 13x + (-8 * x + x * x)) = 5184 (-104 + 13x + (-8x + x2)) = 5184 Combine like terms: 13x + -8x = 5x (-104 + 5x + x2) = 5184 Solving -104 + 5x + x2 = 5184 Solving for variable 'x'. Reorder the terms: -104 + -5184 + 5x + x2 = 5184 + -5184 Combine like terms: -104 + -5184 = -5288 -5288 + 5x + x2 = 5184 + -5184 Combine like terms: 5184 + -5184 = 0 -5288 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5288' to each side of the equation. -5288 + 5x + 5288 + x2 = 0 + 5288 Reorder the terms: -5288 + 5288 + 5x + x2 = 0 + 5288 Combine like terms: -5288 + 5288 = 0 0 + 5x + x2 = 0 + 5288 5x + x2 = 0 + 5288 Combine like terms: 0 + 5288 = 5288 5x + x2 = 5288 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 5288 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 5288 + 6.25 Combine like terms: 5288 + 6.25 = 5294.25 6.25 + 5x + x2 = 5294.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 5294.25 Calculate the square root of the right side: 72.761597014 Break this problem into two subproblems by setting (x + 2.5) equal to 72.761597014 and -72.761597014.Subproblem 1
x + 2.5 = 72.761597014 Simplifying x + 2.5 = 72.761597014 Reorder the terms: 2.5 + x = 72.761597014 Solving 2.5 + x = 72.761597014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 72.761597014 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 72.761597014 + -2.5 x = 72.761597014 + -2.5 Combine like terms: 72.761597014 + -2.5 = 70.261597014 x = 70.261597014 Simplifying x = 70.261597014Subproblem 2
x + 2.5 = -72.761597014 Simplifying x + 2.5 = -72.761597014 Reorder the terms: 2.5 + x = -72.761597014 Solving 2.5 + x = -72.761597014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -72.761597014 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -72.761597014 + -2.5 x = -72.761597014 + -2.5 Combine like terms: -72.761597014 + -2.5 = -75.261597014 x = -75.261597014 Simplifying x = -75.261597014Solution
The solution to the problem is based on the solutions from the subproblems. x = {70.261597014, -75.261597014}
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