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Simplifying (x + 6)(x + 14) = 57 Reorder the terms: (6 + x)(x + 14) = 57 Reorder the terms: (6 + x)(14 + x) = 57 Multiply (6 + x) * (14 + x) (6(14 + x) + x(14 + x)) = 57 ((14 * 6 + x * 6) + x(14 + x)) = 57 ((84 + 6x) + x(14 + x)) = 57 (84 + 6x + (14 * x + x * x)) = 57 (84 + 6x + (14x + x2)) = 57 Combine like terms: 6x + 14x = 20x (84 + 20x + x2) = 57 Solving 84 + 20x + x2 = 57 Solving for variable 'x'. Reorder the terms: 84 + -57 + 20x + x2 = 57 + -57 Combine like terms: 84 + -57 = 27 27 + 20x + x2 = 57 + -57 Combine like terms: 57 + -57 = 0 27 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + 20x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + 20x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 20x + x2 = 0 + -27 20x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 20x + x2 = -27 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -27 + 100 Reorder the terms: 100 + 20x + x2 = -27 + 100 Combine like terms: -27 + 100 = 73 100 + 20x + x2 = 73 Factor a perfect square on the left side: (x + 10)(x + 10) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + 10) equal to 8.544003745 and -8.544003745.Subproblem 1
x + 10 = 8.544003745 Simplifying x + 10 = 8.544003745 Reorder the terms: 10 + x = 8.544003745 Solving 10 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 8.544003745 + -10 Combine like terms: 10 + -10 = 0 0 + x = 8.544003745 + -10 x = 8.544003745 + -10 Combine like terms: 8.544003745 + -10 = -1.455996255 x = -1.455996255 Simplifying x = -1.455996255Subproblem 2
x + 10 = -8.544003745 Simplifying x + 10 = -8.544003745 Reorder the terms: 10 + x = -8.544003745 Solving 10 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -8.544003745 + -10 Combine like terms: 10 + -10 = 0 0 + x = -8.544003745 + -10 x = -8.544003745 + -10 Combine like terms: -8.544003745 + -10 = -18.544003745 x = -18.544003745 Simplifying x = -18.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.455996255, -18.544003745}
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