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Simplifying 50 = 18x + -1x2 Solving 50 = 18x + -1x2 Solving for variable 'x'. Reorder the terms: 50 + -18x + x2 = 18x + -18x + -1x2 + x2 Combine like terms: 18x + -18x = 0 50 + -18x + x2 = 0 + -1x2 + x2 50 + -18x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 50 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -18x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -18x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -18x + x2 = 0 + -50 -18x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -18x + x2 = -50 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 = -50 + 81 Reorder the terms: 81 + -18x + x2 = -50 + 81 Combine like terms: -50 + 81 = 31 81 + -18x + x2 = 31 Factor a perfect square on the left side: (x + -9)(x + -9) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + -9) equal to 5.567764363 and -5.567764363.Subproblem 1
x + -9 = 5.567764363 Simplifying x + -9 = 5.567764363 Reorder the terms: -9 + x = 5.567764363 Solving -9 + x = 5.567764363 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 = 5.567764363 + 9 Combine like terms: -9 + 9 = 0 0 + x = 5.567764363 + 9 x = 5.567764363 + 9 Combine like terms: 5.567764363 + 9 = 14.567764363 x = 14.567764363 Simplifying x = 14.567764363Subproblem 2
x + -9 = -5.567764363 Simplifying x + -9 = -5.567764363 Reorder the terms: -9 + x = -5.567764363 Solving -9 + x = -5.567764363 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 = -5.567764363 + 9 Combine like terms: -9 + 9 = 0 0 + x = -5.567764363 + 9 x = -5.567764363 + 9 Combine like terms: -5.567764363 + 9 = 3.432235637 x = 3.432235637 Simplifying x = 3.432235637Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.567764363, 3.432235637}
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