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Simplifying 34x + -1x2 = 30 Solving 34x + -1x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 34x + -1x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 34x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 30 + -34x + x2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -34x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -34x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -34x + x2 = 0 + -30 -34x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -34x + x2 = -30 The x term is -34x. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34x + 289 + x2 = -30 + 289 Reorder the terms: 289 + -34x + x2 = -30 + 289 Combine like terms: -30 + 289 = 259 289 + -34x + x2 = 259 Factor a perfect square on the left side: (x + -17)(x + -17) = 259 Calculate the square root of the right side: 16.093476939 Break this problem into two subproblems by setting (x + -17) equal to 16.093476939 and -16.093476939.Subproblem 1
x + -17 = 16.093476939 Simplifying x + -17 = 16.093476939 Reorder the terms: -17 + x = 16.093476939 Solving -17 + x = 16.093476939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 16.093476939 + 17 Combine like terms: -17 + 17 = 0 0 + x = 16.093476939 + 17 x = 16.093476939 + 17 Combine like terms: 16.093476939 + 17 = 33.093476939 x = 33.093476939 Simplifying x = 33.093476939Subproblem 2
x + -17 = -16.093476939 Simplifying x + -17 = -16.093476939 Reorder the terms: -17 + x = -16.093476939 Solving -17 + x = -16.093476939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = -16.093476939 + 17 Combine like terms: -17 + 17 = 0 0 + x = -16.093476939 + 17 x = -16.093476939 + 17 Combine like terms: -16.093476939 + 17 = 0.906523061 x = 0.906523061 Simplifying x = 0.906523061Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.093476939, 0.906523061}
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