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Simplifying 19x + 361 = x2 + 9x + 9x + 81 Reorder the terms: 361 + 19x = x2 + 9x + 9x + 81 Reorder the terms: 361 + 19x = 81 + 9x + 9x + x2 Combine like terms: 9x + 9x = 18x 361 + 19x = 81 + 18x + x2 Solving 361 + 19x = 81 + 18x + x2 Solving for variable 'x'. Reorder the terms: 361 + -81 + 19x + -18x + -1x2 = 81 + 18x + x2 + -81 + -18x + -1x2 Combine like terms: 361 + -81 = 280 280 + 19x + -18x + -1x2 = 81 + 18x + x2 + -81 + -18x + -1x2 Combine like terms: 19x + -18x = 1x 280 + 1x + -1x2 = 81 + 18x + x2 + -81 + -18x + -1x2 Reorder the terms: 280 + 1x + -1x2 = 81 + -81 + 18x + -18x + x2 + -1x2 Combine like terms: 81 + -81 = 0 280 + 1x + -1x2 = 0 + 18x + -18x + x2 + -1x2 280 + 1x + -1x2 = 18x + -18x + x2 + -1x2 Combine like terms: 18x + -18x = 0 280 + 1x + -1x2 = 0 + x2 + -1x2 280 + 1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 280 + 1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -280 + -1x + x2 = 0 Move the constant term to the right: Add '280' to each side of the equation. -280 + -1x + 280 + x2 = 0 + 280 Reorder the terms: -280 + 280 + -1x + x2 = 0 + 280 Combine like terms: -280 + 280 = 0 0 + -1x + x2 = 0 + 280 -1x + x2 = 0 + 280 Combine like terms: 0 + 280 = 280 -1x + x2 = 280 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 280 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 280 + 0.25 Combine like terms: 280 + 0.25 = 280.25 0.25 + -1x + x2 = 280.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 280.25 Calculate the square root of the right side: 16.740669043 Break this problem into two subproblems by setting (x + -0.5) equal to 16.740669043 and -16.740669043.Subproblem 1
x + -0.5 = 16.740669043 Simplifying x + -0.5 = 16.740669043 Reorder the terms: -0.5 + x = 16.740669043 Solving -0.5 + x = 16.740669043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 16.740669043 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 16.740669043 + 0.5 x = 16.740669043 + 0.5 Combine like terms: 16.740669043 + 0.5 = 17.240669043 x = 17.240669043 Simplifying x = 17.240669043Subproblem 2
x + -0.5 = -16.740669043 Simplifying x + -0.5 = -16.740669043 Reorder the terms: -0.5 + x = -16.740669043 Solving -0.5 + x = -16.740669043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -16.740669043 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -16.740669043 + 0.5 x = -16.740669043 + 0.5 Combine like terms: -16.740669043 + 0.5 = -16.240669043 x = -16.240669043 Simplifying x = -16.240669043Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.240669043, -16.240669043}
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