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Simplifying (x + -3)(x + 19) = -27 Reorder the terms: (-3 + x)(x + 19) = -27 Reorder the terms: (-3 + x)(19 + x) = -27 Multiply (-3 + x) * (19 + x) (-3(19 + x) + x(19 + x)) = -27 ((19 * -3 + x * -3) + x(19 + x)) = -27 ((-57 + -3x) + x(19 + x)) = -27 (-57 + -3x + (19 * x + x * x)) = -27 (-57 + -3x + (19x + x2)) = -27 Combine like terms: -3x + 19x = 16x (-57 + 16x + x2) = -27 Solving -57 + 16x + x2 = -27 Solving for variable 'x'. Reorder the terms: -57 + 27 + 16x + x2 = -27 + 27 Combine like terms: -57 + 27 = -30 -30 + 16x + x2 = -27 + 27 Combine like terms: -27 + 27 = 0 -30 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 16x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 16x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 16x + x2 = 0 + 30 16x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 16x + x2 = 30 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 30 + 64 Reorder the terms: 64 + 16x + x2 = 30 + 64 Combine like terms: 30 + 64 = 94 64 + 16x + x2 = 94 Factor a perfect square on the left side: (x + 8)(x + 8) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (x + 8) equal to 9.695359715 and -9.695359715.Subproblem 1
x + 8 = 9.695359715 Simplifying x + 8 = 9.695359715 Reorder the terms: 8 + x = 9.695359715 Solving 8 + x = 9.695359715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 9.695359715 + -8 Combine like terms: 8 + -8 = 0 0 + x = 9.695359715 + -8 x = 9.695359715 + -8 Combine like terms: 9.695359715 + -8 = 1.695359715 x = 1.695359715 Simplifying x = 1.695359715Subproblem 2
x + 8 = -9.695359715 Simplifying x + 8 = -9.695359715 Reorder the terms: 8 + x = -9.695359715 Solving 8 + x = -9.695359715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -9.695359715 + -8 Combine like terms: 8 + -8 = 0 0 + x = -9.695359715 + -8 x = -9.695359715 + -8 Combine like terms: -9.695359715 + -8 = -17.695359715 x = -17.695359715 Simplifying x = -17.695359715Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.695359715, -17.695359715}
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