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Simplifying 2(x + 11)(x + -5) = 10000 Reorder the terms: 2(11 + x)(x + -5) = 10000 Reorder the terms: 2(11 + x)(-5 + x) = 10000 Multiply (11 + x) * (-5 + x) 2(11(-5 + x) + x(-5 + x)) = 10000 2((-5 * 11 + x * 11) + x(-5 + x)) = 10000 2((-55 + 11x) + x(-5 + x)) = 10000 2(-55 + 11x + (-5 * x + x * x)) = 10000 2(-55 + 11x + (-5x + x2)) = 10000 Combine like terms: 11x + -5x = 6x 2(-55 + 6x + x2) = 10000 (-55 * 2 + 6x * 2 + x2 * 2) = 10000 (-110 + 12x + 2x2) = 10000 Solving -110 + 12x + 2x2 = 10000 Solving for variable 'x'. Reorder the terms: -110 + -10000 + 12x + 2x2 = 10000 + -10000 Combine like terms: -110 + -10000 = -10110 -10110 + 12x + 2x2 = 10000 + -10000 Combine like terms: 10000 + -10000 = 0 -10110 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5055 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5055 + 6x + x2)' equal to zero and attempt to solve: Simplifying -5055 + 6x + x2 = 0 Solving -5055 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5055' to each side of the equation. -5055 + 6x + 5055 + x2 = 0 + 5055 Reorder the terms: -5055 + 5055 + 6x + x2 = 0 + 5055 Combine like terms: -5055 + 5055 = 0 0 + 6x + x2 = 0 + 5055 6x + x2 = 0 + 5055 Combine like terms: 0 + 5055 = 5055 6x + x2 = 5055 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 5055 + 9 Reorder the terms: 9 + 6x + x2 = 5055 + 9 Combine like terms: 5055 + 9 = 5064 9 + 6x + x2 = 5064 Factor a perfect square on the left side: (x + 3)(x + 3) = 5064 Calculate the square root of the right side: 71.161787499 Break this problem into two subproblems by setting (x + 3) equal to 71.161787499 and -71.161787499.Subproblem 1
x + 3 = 71.161787499 Simplifying x + 3 = 71.161787499 Reorder the terms: 3 + x = 71.161787499 Solving 3 + x = 71.161787499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 71.161787499 + -3 Combine like terms: 3 + -3 = 0 0 + x = 71.161787499 + -3 x = 71.161787499 + -3 Combine like terms: 71.161787499 + -3 = 68.161787499 x = 68.161787499 Simplifying x = 68.161787499Subproblem 2
x + 3 = -71.161787499 Simplifying x + 3 = -71.161787499 Reorder the terms: 3 + x = -71.161787499 Solving 3 + x = -71.161787499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -71.161787499 + -3 Combine like terms: 3 + -3 = 0 0 + x = -71.161787499 + -3 x = -71.161787499 + -3 Combine like terms: -71.161787499 + -3 = -74.161787499 x = -74.161787499 Simplifying x = -74.161787499Solution
The solution to the problem is based on the solutions from the subproblems. x = {68.161787499, -74.161787499}Solution
x = {68.161787499, -74.161787499}
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