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Simplifying 49.06 = (9 + -1x)(9 + -1x) Multiply (9 + -1x) * (9 + -1x) 49.06 = (9(9 + -1x) + -1x * (9 + -1x)) 49.06 = ((9 * 9 + -1x * 9) + -1x * (9 + -1x)) 49.06 = ((81 + -9x) + -1x * (9 + -1x)) 49.06 = (81 + -9x + (9 * -1x + -1x * -1x)) 49.06 = (81 + -9x + (-9x + 1x2)) Combine like terms: -9x + -9x = -18x 49.06 = (81 + -18x + 1x2) Solving 49.06 = 81 + -18x + 1x2 Solving for variable 'x'. Combine like terms: 49.06 + -81 = -31.94 -31.94 + 18x + -1x2 = 81 + -18x + 1x2 + -81 + 18x + -1x2 Reorder the terms: -31.94 + 18x + -1x2 = 81 + -81 + -18x + 18x + 1x2 + -1x2 Combine like terms: 81 + -81 = 0 -31.94 + 18x + -1x2 = 0 + -18x + 18x + 1x2 + -1x2 -31.94 + 18x + -1x2 = -18x + 18x + 1x2 + -1x2 Combine like terms: -18x + 18x = 0 -31.94 + 18x + -1x2 = 0 + 1x2 + -1x2 -31.94 + 18x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 -31.94 + 18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 31.94 + -18x + x2 = 0 Move the constant term to the right: Add '-31.94' to each side of the equation. 31.94 + -18x + -31.94 + x2 = 0 + -31.94 Reorder the terms: 31.94 + -31.94 + -18x + x2 = 0 + -31.94 Combine like terms: 31.94 + -31.94 = 0.00 0.00 + -18x + x2 = 0 + -31.94 -18x + x2 = 0 + -31.94 Combine like terms: 0 + -31.94 = -31.94 -18x + x2 = -31.94 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 = -31.94 + 81 Reorder the terms: 81 + -18x + x2 = -31.94 + 81 Combine like terms: -31.94 + 81 = 49.06 81 + -18x + x2 = 49.06 Factor a perfect square on the left side: (x + -9)(x + -9) = 49.06 Calculate the square root of the right side: 7.004284403 Break this problem into two subproblems by setting (x + -9) equal to 7.004284403 and -7.004284403.Subproblem 1
x + -9 = 7.004284403 Simplifying x + -9 = 7.004284403 Reorder the terms: -9 + x = 7.004284403 Solving -9 + x = 7.004284403 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 = 7.004284403 + 9 Combine like terms: -9 + 9 = 0 0 + x = 7.004284403 + 9 x = 7.004284403 + 9 Combine like terms: 7.004284403 + 9 = 16.004284403 x = 16.004284403 Simplifying x = 16.004284403Subproblem 2
x + -9 = -7.004284403 Simplifying x + -9 = -7.004284403 Reorder the terms: -9 + x = -7.004284403 Solving -9 + x = -7.004284403 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 = -7.004284403 + 9 Combine like terms: -9 + 9 = 0 0 + x = -7.004284403 + 9 x = -7.004284403 + 9 Combine like terms: -7.004284403 + 9 = 1.995715597 x = 1.995715597 Simplifying x = 1.995715597Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.004284403, 1.995715597}
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