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Simplifying 17x2 + -7 = 34x + 101 Reorder the terms: -7 + 17x2 = 34x + 101 Reorder the terms: -7 + 17x2 = 101 + 34x Solving -7 + 17x2 = 101 + 34x Solving for variable 'x'. Reorder the terms: -7 + -101 + -34x + 17x2 = 101 + 34x + -101 + -34x Combine like terms: -7 + -101 = -108 -108 + -34x + 17x2 = 101 + 34x + -101 + -34x Reorder the terms: -108 + -34x + 17x2 = 101 + -101 + 34x + -34x Combine like terms: 101 + -101 = 0 -108 + -34x + 17x2 = 0 + 34x + -34x -108 + -34x + 17x2 = 34x + -34x Combine like terms: 34x + -34x = 0 -108 + -34x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -6.352941176 + -2x + x2 = 0 Move the constant term to the right: Add '6.352941176' to each side of the equation. -6.352941176 + -2x + 6.352941176 + x2 = 0 + 6.352941176 Reorder the terms: -6.352941176 + 6.352941176 + -2x + x2 = 0 + 6.352941176 Combine like terms: -6.352941176 + 6.352941176 = 0.000000000 0.000000000 + -2x + x2 = 0 + 6.352941176 -2x + x2 = 0 + 6.352941176 Combine like terms: 0 + 6.352941176 = 6.352941176 -2x + x2 = 6.352941176 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 6.352941176 + 1 Reorder the terms: 1 + -2x + x2 = 6.352941176 + 1 Combine like terms: 6.352941176 + 1 = 7.352941176 1 + -2x + x2 = 7.352941176 Factor a perfect square on the left side: (x + -1)(x + -1) = 7.352941176 Calculate the square root of the right side: 2.711630723 Break this problem into two subproblems by setting (x + -1) equal to 2.711630723 and -2.711630723.Subproblem 1
x + -1 = 2.711630723 Simplifying x + -1 = 2.711630723 Reorder the terms: -1 + x = 2.711630723 Solving -1 + x = 2.711630723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.711630723 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.711630723 + 1 x = 2.711630723 + 1 Combine like terms: 2.711630723 + 1 = 3.711630723 x = 3.711630723 Simplifying x = 3.711630723Subproblem 2
x + -1 = -2.711630723 Simplifying x + -1 = -2.711630723 Reorder the terms: -1 + x = -2.711630723 Solving -1 + x = -2.711630723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.711630723 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.711630723 + 1 x = -2.711630723 + 1 Combine like terms: -2.711630723 + 1 = -1.711630723 x = -1.711630723 Simplifying x = -1.711630723Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.711630723, -1.711630723}
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