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Simplifying (8 + -1x)(10 + -1x) = 50 Multiply (8 + -1x) * (10 + -1x) (8(10 + -1x) + -1x * (10 + -1x)) = 50 ((10 * 8 + -1x * 8) + -1x * (10 + -1x)) = 50 ((80 + -8x) + -1x * (10 + -1x)) = 50 (80 + -8x + (10 * -1x + -1x * -1x)) = 50 (80 + -8x + (-10x + 1x2)) = 50 Combine like terms: -8x + -10x = -18x (80 + -18x + 1x2) = 50 Solving 80 + -18x + 1x2 = 50 Solving for variable 'x'. Reorder the terms: 80 + -50 + -18x + 1x2 = 50 + -50 Combine like terms: 80 + -50 = 30 30 + -18x + 1x2 = 50 + -50 Combine like terms: 50 + -50 = 0 30 + -18x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -18x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -18x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -18x + x2 = 0 + -30 -18x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -18x + x2 = -30 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 = -30 + 81 Reorder the terms: 81 + -18x + x2 = -30 + 81 Combine like terms: -30 + 81 = 51 81 + -18x + x2 = 51 Factor a perfect square on the left side: (x + -9)(x + -9) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (x + -9) equal to 7.141428429 and -7.141428429.Subproblem 1
x + -9 = 7.141428429 Simplifying x + -9 = 7.141428429 Reorder the terms: -9 + x = 7.141428429 Solving -9 + x = 7.141428429 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 = 7.141428429 + 9 Combine like terms: -9 + 9 = 0 0 + x = 7.141428429 + 9 x = 7.141428429 + 9 Combine like terms: 7.141428429 + 9 = 16.141428429 x = 16.141428429 Simplifying x = 16.141428429Subproblem 2
x + -9 = -7.141428429 Simplifying x + -9 = -7.141428429 Reorder the terms: -9 + x = -7.141428429 Solving -9 + x = -7.141428429 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 = -7.141428429 + 9 Combine like terms: -9 + 9 = 0 0 + x = -7.141428429 + 9 x = -7.141428429 + 9 Combine like terms: -7.141428429 + 9 = 1.858571571 x = 1.858571571 Simplifying x = 1.858571571Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.141428429, 1.858571571}
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