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Simplifying 0.35x2 + -329x + 975 = 1339 Reorder the terms: 975 + -329x + 0.35x2 = 1339 Solving 975 + -329x + 0.35x2 = 1339 Solving for variable 'x'. Reorder the terms: 975 + -1339 + -329x + 0.35x2 = 1339 + -1339 Combine like terms: 975 + -1339 = -364 -364 + -329x + 0.35x2 = 1339 + -1339 Combine like terms: 1339 + -1339 = 0 -364 + -329x + 0.35x2 = 0 Begin completing the square. Divide all terms by 0.35 the coefficient of the squared term: Divide each side by '0.35'. -1040 + -940x + x2 = 0 Move the constant term to the right: Add '1040' to each side of the equation. -1040 + -940x + 1040 + x2 = 0 + 1040 Reorder the terms: -1040 + 1040 + -940x + x2 = 0 + 1040 Combine like terms: -1040 + 1040 = 0 0 + -940x + x2 = 0 + 1040 -940x + x2 = 0 + 1040 Combine like terms: 0 + 1040 = 1040 -940x + x2 = 1040 The x term is -940x. Take half its coefficient (-470). Square it (220900) and add it to both sides. Add '220900' to each side of the equation. -940x + 220900 + x2 = 1040 + 220900 Reorder the terms: 220900 + -940x + x2 = 1040 + 220900 Combine like terms: 1040 + 220900 = 221940 220900 + -940x + x2 = 221940 Factor a perfect square on the left side: (x + -470)(x + -470) = 221940 Calculate the square root of the right side: 471.105083819 Break this problem into two subproblems by setting (x + -470) equal to 471.105083819 and -471.105083819.Subproblem 1
x + -470 = 471.105083819 Simplifying x + -470 = 471.105083819 Reorder the terms: -470 + x = 471.105083819 Solving -470 + x = 471.105083819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '470' to each side of the equation. -470 + 470 + x = 471.105083819 + 470 Combine like terms: -470 + 470 = 0 0 + x = 471.105083819 + 470 x = 471.105083819 + 470 Combine like terms: 471.105083819 + 470 = 941.105083819 x = 941.105083819 Simplifying x = 941.105083819Subproblem 2
x + -470 = -471.105083819 Simplifying x + -470 = -471.105083819 Reorder the terms: -470 + x = -471.105083819 Solving -470 + x = -471.105083819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '470' to each side of the equation. -470 + 470 + x = -471.105083819 + 470 Combine like terms: -470 + 470 = 0 0 + x = -471.105083819 + 470 x = -471.105083819 + 470 Combine like terms: -471.105083819 + 470 = -1.105083819 x = -1.105083819 Simplifying x = -1.105083819Solution
The solution to the problem is based on the solutions from the subproblems. x = {941.105083819, -1.105083819}
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