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Simplifying 2X * X + 3X + -213 = 329 Multiply X * X 2X2 + 3X + -213 = 329 Reorder the terms: -213 + 3X + 2X2 = 329 Solving -213 + 3X + 2X2 = 329 Solving for variable 'X'. Reorder the terms: -213 + -329 + 3X + 2X2 = 329 + -329 Combine like terms: -213 + -329 = -542 -542 + 3X + 2X2 = 329 + -329 Combine like terms: 329 + -329 = 0 -542 + 3X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -271 + 1.5X + X2 = 0 Move the constant term to the right: Add '271' to each side of the equation. -271 + 1.5X + 271 + X2 = 0 + 271 Reorder the terms: -271 + 271 + 1.5X + X2 = 0 + 271 Combine like terms: -271 + 271 = 0 0 + 1.5X + X2 = 0 + 271 1.5X + X2 = 0 + 271 Combine like terms: 0 + 271 = 271 1.5X + X2 = 271 The X term is 1.5X. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5X + 0.5625 + X2 = 271 + 0.5625 Reorder the terms: 0.5625 + 1.5X + X2 = 271 + 0.5625 Combine like terms: 271 + 0.5625 = 271.5625 0.5625 + 1.5X + X2 = 271.5625 Factor a perfect square on the left side: (X + 0.75)(X + 0.75) = 271.5625 Calculate the square root of the right side: 16.479153498 Break this problem into two subproblems by setting (X + 0.75) equal to 16.479153498 and -16.479153498.Subproblem 1
X + 0.75 = 16.479153498 Simplifying X + 0.75 = 16.479153498 Reorder the terms: 0.75 + X = 16.479153498 Solving 0.75 + X = 16.479153498 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + X = 16.479153498 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + X = 16.479153498 + -0.75 X = 16.479153498 + -0.75 Combine like terms: 16.479153498 + -0.75 = 15.729153498 X = 15.729153498 Simplifying X = 15.729153498Subproblem 2
X + 0.75 = -16.479153498 Simplifying X + 0.75 = -16.479153498 Reorder the terms: 0.75 + X = -16.479153498 Solving 0.75 + X = -16.479153498 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + X = -16.479153498 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + X = -16.479153498 + -0.75 X = -16.479153498 + -0.75 Combine like terms: -16.479153498 + -0.75 = -17.229153498 X = -17.229153498 Simplifying X = -17.229153498Solution
The solution to the problem is based on the solutions from the subproblems. X = {15.729153498, -17.229153498}
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