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Simplifying (x + 8)(x + 10) = 244 Reorder the terms: (8 + x)(x + 10) = 244 Reorder the terms: (8 + x)(10 + x) = 244 Multiply (8 + x) * (10 + x) (8(10 + x) + x(10 + x)) = 244 ((10 * 8 + x * 8) + x(10 + x)) = 244 ((80 + 8x) + x(10 + x)) = 244 (80 + 8x + (10 * x + x * x)) = 244 (80 + 8x + (10x + x2)) = 244 Combine like terms: 8x + 10x = 18x (80 + 18x + x2) = 244 Solving 80 + 18x + x2 = 244 Solving for variable 'x'. Reorder the terms: 80 + -244 + 18x + x2 = 244 + -244 Combine like terms: 80 + -244 = -164 -164 + 18x + x2 = 244 + -244 Combine like terms: 244 + -244 = 0 -164 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '164' to each side of the equation. -164 + 18x + 164 + x2 = 0 + 164 Reorder the terms: -164 + 164 + 18x + x2 = 0 + 164 Combine like terms: -164 + 164 = 0 0 + 18x + x2 = 0 + 164 18x + x2 = 0 + 164 Combine like terms: 0 + 164 = 164 18x + x2 = 164 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 = 164 + 81 Reorder the terms: 81 + 18x + x2 = 164 + 81 Combine like terms: 164 + 81 = 245 81 + 18x + x2 = 245 Factor a perfect square on the left side: (x + 9)(x + 9) = 245 Calculate the square root of the right side: 15.652475842 Break this problem into two subproblems by setting (x + 9) equal to 15.652475842 and -15.652475842.Subproblem 1
x + 9 = 15.652475842 Simplifying x + 9 = 15.652475842 Reorder the terms: 9 + x = 15.652475842 Solving 9 + x = 15.652475842 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 = 15.652475842 + -9 Combine like terms: 9 + -9 = 0 0 + x = 15.652475842 + -9 x = 15.652475842 + -9 Combine like terms: 15.652475842 + -9 = 6.652475842 x = 6.652475842 Simplifying x = 6.652475842Subproblem 2
x + 9 = -15.652475842 Simplifying x + 9 = -15.652475842 Reorder the terms: 9 + x = -15.652475842 Solving 9 + x = -15.652475842 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 = -15.652475842 + -9 Combine like terms: 9 + -9 = 0 0 + x = -15.652475842 + -9 x = -15.652475842 + -9 Combine like terms: -15.652475842 + -9 = -24.652475842 x = -24.652475842 Simplifying x = -24.652475842Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.652475842, -24.652475842}
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