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Simplifying (x + -6)(x + -3) = 10000 Reorder the terms: (-6 + x)(x + -3) = 10000 Reorder the terms: (-6 + x)(-3 + x) = 10000 Multiply (-6 + x) * (-3 + x) (-6(-3 + x) + x(-3 + x)) = 10000 ((-3 * -6 + x * -6) + x(-3 + x)) = 10000 ((18 + -6x) + x(-3 + x)) = 10000 (18 + -6x + (-3 * x + x * x)) = 10000 (18 + -6x + (-3x + x2)) = 10000 Combine like terms: -6x + -3x = -9x (18 + -9x + x2) = 10000 Solving 18 + -9x + x2 = 10000 Solving for variable 'x'. Reorder the terms: 18 + -10000 + -9x + x2 = 10000 + -10000 Combine like terms: 18 + -10000 = -9982 -9982 + -9x + x2 = 10000 + -10000 Combine like terms: 10000 + -10000 = 0 -9982 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9982' to each side of the equation. -9982 + -9x + 9982 + x2 = 0 + 9982 Reorder the terms: -9982 + 9982 + -9x + x2 = 0 + 9982 Combine like terms: -9982 + 9982 = 0 0 + -9x + x2 = 0 + 9982 -9x + x2 = 0 + 9982 Combine like terms: 0 + 9982 = 9982 -9x + x2 = 9982 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 9982 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 9982 + 20.25 Combine like terms: 9982 + 20.25 = 10002.25 20.25 + -9x + x2 = 10002.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 10002.25 Calculate the square root of the right side: 100.011249367 Break this problem into two subproblems by setting (x + -4.5) equal to 100.011249367 and -100.011249367.Subproblem 1
x + -4.5 = 100.011249367 Simplifying x + -4.5 = 100.011249367 Reorder the terms: -4.5 + x = 100.011249367 Solving -4.5 + x = 100.011249367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 100.011249367 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 100.011249367 + 4.5 x = 100.011249367 + 4.5 Combine like terms: 100.011249367 + 4.5 = 104.511249367 x = 104.511249367 Simplifying x = 104.511249367Subproblem 2
x + -4.5 = -100.011249367 Simplifying x + -4.5 = -100.011249367 Reorder the terms: -4.5 + x = -100.011249367 Solving -4.5 + x = -100.011249367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -100.011249367 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -100.011249367 + 4.5 x = -100.011249367 + 4.5 Combine like terms: -100.011249367 + 4.5 = -95.511249367 x = -95.511249367 Simplifying x = -95.511249367Solution
The solution to the problem is based on the solutions from the subproblems. x = {104.511249367, -95.511249367}
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