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Simplifying (9 + x)(8 + x) = 144 Multiply (9 + x) * (8 + x) (9(8 + x) + x(8 + x)) = 144 ((8 * 9 + x * 9) + x(8 + x)) = 144 ((72 + 9x) + x(8 + x)) = 144 (72 + 9x + (8 * x + x * x)) = 144 (72 + 9x + (8x + x2)) = 144 Combine like terms: 9x + 8x = 17x (72 + 17x + x2) = 144 Solving 72 + 17x + x2 = 144 Solving for variable 'x'. Reorder the terms: 72 + -144 + 17x + x2 = 144 + -144 Combine like terms: 72 + -144 = -72 -72 + 17x + x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -72 + 17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 17x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 17x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 17x + x2 = 0 + 72 17x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 17x + x2 = 72 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 72 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 72 + 72.25 Combine like terms: 72 + 72.25 = 144.25 72.25 + 17x + x2 = 144.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 144.25 Calculate the square root of the right side: 12.010412149 Break this problem into two subproblems by setting (x + 8.5) equal to 12.010412149 and -12.010412149.Subproblem 1
x + 8.5 = 12.010412149 Simplifying x + 8.5 = 12.010412149 Reorder the terms: 8.5 + x = 12.010412149 Solving 8.5 + x = 12.010412149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 12.010412149 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 12.010412149 + -8.5 x = 12.010412149 + -8.5 Combine like terms: 12.010412149 + -8.5 = 3.510412149 x = 3.510412149 Simplifying x = 3.510412149Subproblem 2
x + 8.5 = -12.010412149 Simplifying x + 8.5 = -12.010412149 Reorder the terms: 8.5 + x = -12.010412149 Solving 8.5 + x = -12.010412149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -12.010412149 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -12.010412149 + -8.5 x = -12.010412149 + -8.5 Combine like terms: -12.010412149 + -8.5 = -20.510412149 x = -20.510412149 Simplifying x = -20.510412149Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.510412149, -20.510412149}
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