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Simplifying 29x2 + -58x + -42 = 0 Reorder the terms: -42 + -58x + 29x2 = 0 Solving -42 + -58x + 29x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 29 the coefficient of the squared term: Divide each side by '29'. -1.448275862 + -2x + x2 = 0 Move the constant term to the right: Add '1.448275862' to each side of the equation. -1.448275862 + -2x + 1.448275862 + x2 = 0 + 1.448275862 Reorder the terms: -1.448275862 + 1.448275862 + -2x + x2 = 0 + 1.448275862 Combine like terms: -1.448275862 + 1.448275862 = 0.000000000 0.000000000 + -2x + x2 = 0 + 1.448275862 -2x + x2 = 0 + 1.448275862 Combine like terms: 0 + 1.448275862 = 1.448275862 -2x + x2 = 1.448275862 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 = 1.448275862 + 1 Reorder the terms: 1 + -2x + x2 = 1.448275862 + 1 Combine like terms: 1.448275862 + 1 = 2.448275862 1 + -2x + x2 = 2.448275862 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.448275862 Calculate the square root of the right side: 1.564696732 Break this problem into two subproblems by setting (x + -1) equal to 1.564696732 and -1.564696732.Subproblem 1
x + -1 = 1.564696732 Simplifying x + -1 = 1.564696732 Reorder the terms: -1 + x = 1.564696732 Solving -1 + x = 1.564696732 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 = 1.564696732 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.564696732 + 1 x = 1.564696732 + 1 Combine like terms: 1.564696732 + 1 = 2.564696732 x = 2.564696732 Simplifying x = 2.564696732Subproblem 2
x + -1 = -1.564696732 Simplifying x + -1 = -1.564696732 Reorder the terms: -1 + x = -1.564696732 Solving -1 + x = -1.564696732 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 = -1.564696732 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.564696732 + 1 x = -1.564696732 + 1 Combine like terms: -1.564696732 + 1 = -0.564696732 x = -0.564696732 Simplifying x = -0.564696732Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.564696732, -0.564696732}
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