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Simplifying x2 + 3x + -61 = 0 Reorder the terms: -61 + 3x + x2 = 0 Solving -61 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '61' to each side of the equation. -61 + 3x + 61 + x2 = 0 + 61 Reorder the terms: -61 + 61 + 3x + x2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + 3x + x2 = 0 + 61 3x + x2 = 0 + 61 Combine like terms: 0 + 61 = 61 3x + x2 = 61 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 61 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 61 + 2.25 Combine like terms: 61 + 2.25 = 63.25 2.25 + 3x + x2 = 63.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 63.25 Calculate the square root of the right side: 7.95298686 Break this problem into two subproblems by setting (x + 1.5) equal to 7.95298686 and -7.95298686.Subproblem 1
x + 1.5 = 7.95298686 Simplifying x + 1.5 = 7.95298686 Reorder the terms: 1.5 + x = 7.95298686 Solving 1.5 + x = 7.95298686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 7.95298686 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.95298686 + -1.5 x = 7.95298686 + -1.5 Combine like terms: 7.95298686 + -1.5 = 6.45298686 x = 6.45298686 Simplifying x = 6.45298686Subproblem 2
x + 1.5 = -7.95298686 Simplifying x + 1.5 = -7.95298686 Reorder the terms: 1.5 + x = -7.95298686 Solving 1.5 + x = -7.95298686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -7.95298686 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.95298686 + -1.5 x = -7.95298686 + -1.5 Combine like terms: -7.95298686 + -1.5 = -9.45298686 x = -9.45298686 Simplifying x = -9.45298686Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.45298686, -9.45298686}
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