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Simplifying 2x(x + -33) + x = 162 Reorder the terms: 2x(-33 + x) + x = 162 (-33 * 2x + x * 2x) + x = 162 (-66x + 2x2) + x = 162 Reorder the terms: -66x + x + 2x2 = 162 Combine like terms: -66x + x = -65x -65x + 2x2 = 162 Solving -65x + 2x2 = 162 Solving for variable 'x'. Reorder the terms: -162 + -65x + 2x2 = 162 + -162 Combine like terms: 162 + -162 = 0 -162 + -65x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -81 + -32.5x + x2 = 0 Move the constant term to the right: Add '81' to each side of the equation. -81 + -32.5x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + -32.5x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -32.5x + x2 = 0 + 81 -32.5x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 -32.5x + x2 = 81 The x term is -32.5x. Take half its coefficient (-16.25). Square it (264.0625) and add it to both sides. Add '264.0625' to each side of the equation. -32.5x + 264.0625 + x2 = 81 + 264.0625 Reorder the terms: 264.0625 + -32.5x + x2 = 81 + 264.0625 Combine like terms: 81 + 264.0625 = 345.0625 264.0625 + -32.5x + x2 = 345.0625 Factor a perfect square on the left side: (x + -16.25)(x + -16.25) = 345.0625 Calculate the square root of the right side: 18.575857988 Break this problem into two subproblems by setting (x + -16.25) equal to 18.575857988 and -18.575857988.Subproblem 1
x + -16.25 = 18.575857988 Simplifying x + -16.25 = 18.575857988 Reorder the terms: -16.25 + x = 18.575857988 Solving -16.25 + x = 18.575857988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.25' to each side of the equation. -16.25 + 16.25 + x = 18.575857988 + 16.25 Combine like terms: -16.25 + 16.25 = 0.00 0.00 + x = 18.575857988 + 16.25 x = 18.575857988 + 16.25 Combine like terms: 18.575857988 + 16.25 = 34.825857988 x = 34.825857988 Simplifying x = 34.825857988Subproblem 2
x + -16.25 = -18.575857988 Simplifying x + -16.25 = -18.575857988 Reorder the terms: -16.25 + x = -18.575857988 Solving -16.25 + x = -18.575857988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.25' to each side of the equation. -16.25 + 16.25 + x = -18.575857988 + 16.25 Combine like terms: -16.25 + 16.25 = 0.00 0.00 + x = -18.575857988 + 16.25 x = -18.575857988 + 16.25 Combine like terms: -18.575857988 + 16.25 = -2.325857988 x = -2.325857988 Simplifying x = -2.325857988Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.825857988, -2.325857988}
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