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Simplifying (8 + x)(10 + x) = 152 Multiply (8 + x) * (10 + x) (8(10 + x) + x(10 + x)) = 152 ((10 * 8 + x * 8) + x(10 + x)) = 152 ((80 + 8x) + x(10 + x)) = 152 (80 + 8x + (10 * x + x * x)) = 152 (80 + 8x + (10x + x2)) = 152 Combine like terms: 8x + 10x = 18x (80 + 18x + x2) = 152 Solving 80 + 18x + x2 = 152 Solving for variable 'x'. Reorder the terms: 80 + -152 + 18x + x2 = 152 + -152 Combine like terms: 80 + -152 = -72 -72 + 18x + x2 = 152 + -152 Combine like terms: 152 + -152 = 0 -72 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 18x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 18x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 18x + x2 = 0 + 72 18x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 18x + x2 = 72 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 72 + 81 Reorder the terms: 81 + 18x + x2 = 72 + 81 Combine like terms: 72 + 81 = 153 81 + 18x + x2 = 153 Factor a perfect square on the left side: (x + 9)(x + 9) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (x + 9) equal to 12.369316877 and -12.369316877.Subproblem 1
x + 9 = 12.369316877 Simplifying x + 9 = 12.369316877 Reorder the terms: 9 + x = 12.369316877 Solving 9 + x = 12.369316877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 12.369316877 + -9 Combine like terms: 9 + -9 = 0 0 + x = 12.369316877 + -9 x = 12.369316877 + -9 Combine like terms: 12.369316877 + -9 = 3.369316877 x = 3.369316877 Simplifying x = 3.369316877Subproblem 2
x + 9 = -12.369316877 Simplifying x + 9 = -12.369316877 Reorder the terms: 9 + x = -12.369316877 Solving 9 + x = -12.369316877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -12.369316877 + -9 Combine like terms: 9 + -9 = 0 0 + x = -12.369316877 + -9 x = -12.369316877 + -9 Combine like terms: -12.369316877 + -9 = -21.369316877 x = -21.369316877 Simplifying x = -21.369316877Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.369316877, -21.369316877}
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