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Simplifying 29x2 + 15x + -27 = 0 Reorder the terms: -27 + 15x + 29x2 = 0 Solving -27 + 15x + 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'. -0.9310344828 + 0.5172413793x + x2 = 0 Move the constant term to the right: Add '0.9310344828' to each side of the equation. -0.9310344828 + 0.5172413793x + 0.9310344828 + x2 = 0 + 0.9310344828 Reorder the terms: -0.9310344828 + 0.9310344828 + 0.5172413793x + x2 = 0 + 0.9310344828 Combine like terms: -0.9310344828 + 0.9310344828 = 0.0000000000 0.0000000000 + 0.5172413793x + x2 = 0 + 0.9310344828 0.5172413793x + x2 = 0 + 0.9310344828 Combine like terms: 0 + 0.9310344828 = 0.9310344828 0.5172413793x + x2 = 0.9310344828 The x term is 0.5172413793x. Take half its coefficient (0.2586206897). Square it (0.06688466114) and add it to both sides. Add '0.06688466114' to each side of the equation. 0.5172413793x + 0.06688466114 + x2 = 0.9310344828 + 0.06688466114 Reorder the terms: 0.06688466114 + 0.5172413793x + x2 = 0.9310344828 + 0.06688466114 Combine like terms: 0.9310344828 + 0.06688466114 = 0.99791914394 0.06688466114 + 0.5172413793x + x2 = 0.99791914394 Factor a perfect square on the left side: (x + 0.2586206897)(x + 0.2586206897) = 0.99791914394 Calculate the square root of the right side: 0.99895903 Break this problem into two subproblems by setting (x + 0.2586206897) equal to 0.99895903 and -0.99895903.Subproblem 1
x + 0.2586206897 = 0.99895903 Simplifying x + 0.2586206897 = 0.99895903 Reorder the terms: 0.2586206897 + x = 0.99895903 Solving 0.2586206897 + x = 0.99895903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2586206897' to each side of the equation. 0.2586206897 + -0.2586206897 + x = 0.99895903 + -0.2586206897 Combine like terms: 0.2586206897 + -0.2586206897 = 0.0000000000 0.0000000000 + x = 0.99895903 + -0.2586206897 x = 0.99895903 + -0.2586206897 Combine like terms: 0.99895903 + -0.2586206897 = 0.7403383403 x = 0.7403383403 Simplifying x = 0.7403383403Subproblem 2
x + 0.2586206897 = -0.99895903 Simplifying x + 0.2586206897 = -0.99895903 Reorder the terms: 0.2586206897 + x = -0.99895903 Solving 0.2586206897 + x = -0.99895903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2586206897' to each side of the equation. 0.2586206897 + -0.2586206897 + x = -0.99895903 + -0.2586206897 Combine like terms: 0.2586206897 + -0.2586206897 = 0.0000000000 0.0000000000 + x = -0.99895903 + -0.2586206897 x = -0.99895903 + -0.2586206897 Combine like terms: -0.99895903 + -0.2586206897 = -1.2575797197 x = -1.2575797197 Simplifying x = -1.2575797197Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7403383403, -1.2575797197}
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