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Simplifying x2 + 103x + -30 = 0 Reorder the terms: -30 + 103x + x2 = 0 Solving -30 + 103x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 103x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 103x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 103x + x2 = 0 + 30 103x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 103x + x2 = 30 The x term is 103x. Take half its coefficient (51.5). Square it (2652.25) and add it to both sides. Add '2652.25' to each side of the equation. 103x + 2652.25 + x2 = 30 + 2652.25 Reorder the terms: 2652.25 + 103x + x2 = 30 + 2652.25 Combine like terms: 30 + 2652.25 = 2682.25 2652.25 + 103x + x2 = 2682.25 Factor a perfect square on the left side: (x + 51.5)(x + 51.5) = 2682.25 Calculate the square root of the right side: 51.790443134 Break this problem into two subproblems by setting (x + 51.5) equal to 51.790443134 and -51.790443134.Subproblem 1
x + 51.5 = 51.790443134 Simplifying x + 51.5 = 51.790443134 Reorder the terms: 51.5 + x = 51.790443134 Solving 51.5 + x = 51.790443134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-51.5' to each side of the equation. 51.5 + -51.5 + x = 51.790443134 + -51.5 Combine like terms: 51.5 + -51.5 = 0.0 0.0 + x = 51.790443134 + -51.5 x = 51.790443134 + -51.5 Combine like terms: 51.790443134 + -51.5 = 0.290443134 x = 0.290443134 Simplifying x = 0.290443134Subproblem 2
x + 51.5 = -51.790443134 Simplifying x + 51.5 = -51.790443134 Reorder the terms: 51.5 + x = -51.790443134 Solving 51.5 + x = -51.790443134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-51.5' to each side of the equation. 51.5 + -51.5 + x = -51.790443134 + -51.5 Combine like terms: 51.5 + -51.5 = 0.0 0.0 + x = -51.790443134 + -51.5 x = -51.790443134 + -51.5 Combine like terms: -51.790443134 + -51.5 = -103.290443134 x = -103.290443134 Simplifying x = -103.290443134Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.290443134, -103.290443134}
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