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Simplifying 10x2 + -34x + -1 = 0 Reorder the terms: -1 + -34x + 10x2 = 0 Solving -1 + -34x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.1 + -3.4x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -3.4x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + -3.4x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -3.4x + x2 = 0 + 0.1 -3.4x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 -3.4x + x2 = 0.1 The x term is -3.4x. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4x + 2.89 + x2 = 0.1 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 0.1 + 2.89 Combine like terms: 0.1 + 2.89 = 2.99 2.89 + -3.4x + x2 = 2.99 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 2.99 Calculate the square root of the right side: 1.729161647 Break this problem into two subproblems by setting (x + -1.7) equal to 1.729161647 and -1.729161647.Subproblem 1
x + -1.7 = 1.729161647 Simplifying x + -1.7 = 1.729161647 Reorder the terms: -1.7 + x = 1.729161647 Solving -1.7 + x = 1.729161647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = 1.729161647 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 1.729161647 + 1.7 x = 1.729161647 + 1.7 Combine like terms: 1.729161647 + 1.7 = 3.429161647 x = 3.429161647 Simplifying x = 3.429161647Subproblem 2
x + -1.7 = -1.729161647 Simplifying x + -1.7 = -1.729161647 Reorder the terms: -1.7 + x = -1.729161647 Solving -1.7 + x = -1.729161647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = -1.729161647 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -1.729161647 + 1.7 x = -1.729161647 + 1.7 Combine like terms: -1.729161647 + 1.7 = -0.029161647 x = -0.029161647 Simplifying x = -0.029161647Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.429161647, -0.029161647}
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