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Simplifying (x + 8)(x + -2) = 121 Reorder the terms: (8 + x)(x + -2) = 121 Reorder the terms: (8 + x)(-2 + x) = 121 Multiply (8 + x) * (-2 + x) (8(-2 + x) + x(-2 + x)) = 121 ((-2 * 8 + x * 8) + x(-2 + x)) = 121 ((-16 + 8x) + x(-2 + x)) = 121 (-16 + 8x + (-2 * x + x * x)) = 121 (-16 + 8x + (-2x + x2)) = 121 Combine like terms: 8x + -2x = 6x (-16 + 6x + x2) = 121 Solving -16 + 6x + x2 = 121 Solving for variable 'x'. Reorder the terms: -16 + -121 + 6x + x2 = 121 + -121 Combine like terms: -16 + -121 = -137 -137 + 6x + x2 = 121 + -121 Combine like terms: 121 + -121 = 0 -137 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '137' to each side of the equation. -137 + 6x + 137 + x2 = 0 + 137 Reorder the terms: -137 + 137 + 6x + x2 = 0 + 137 Combine like terms: -137 + 137 = 0 0 + 6x + x2 = 0 + 137 6x + x2 = 0 + 137 Combine like terms: 0 + 137 = 137 6x + x2 = 137 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 = 137 + 9 Reorder the terms: 9 + 6x + x2 = 137 + 9 Combine like terms: 137 + 9 = 146 9 + 6x + x2 = 146 Factor a perfect square on the left side: (x + 3)(x + 3) = 146 Calculate the square root of the right side: 12.083045974 Break this problem into two subproblems by setting (x + 3) equal to 12.083045974 and -12.083045974.Subproblem 1
x + 3 = 12.083045974 Simplifying x + 3 = 12.083045974 Reorder the terms: 3 + x = 12.083045974 Solving 3 + x = 12.083045974 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 = 12.083045974 + -3 Combine like terms: 3 + -3 = 0 0 + x = 12.083045974 + -3 x = 12.083045974 + -3 Combine like terms: 12.083045974 + -3 = 9.083045974 x = 9.083045974 Simplifying x = 9.083045974Subproblem 2
x + 3 = -12.083045974 Simplifying x + 3 = -12.083045974 Reorder the terms: 3 + x = -12.083045974 Solving 3 + x = -12.083045974 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 = -12.083045974 + -3 Combine like terms: 3 + -3 = 0 0 + x = -12.083045974 + -3 x = -12.083045974 + -3 Combine like terms: -12.083045974 + -3 = -15.083045974 x = -15.083045974 Simplifying x = -15.083045974Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.083045974, -15.083045974}
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