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Simplifying 2x2 + -4x + -103 = 0 Reorder the terms: -103 + -4x + 2x2 = 0 Solving -103 + -4x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -51.5 + -2x + x2 = 0 Move the constant term to the right: Add '51.5' to each side of the equation. -51.5 + -2x + 51.5 + x2 = 0 + 51.5 Reorder the terms: -51.5 + 51.5 + -2x + x2 = 0 + 51.5 Combine like terms: -51.5 + 51.5 = 0.0 0.0 + -2x + x2 = 0 + 51.5 -2x + x2 = 0 + 51.5 Combine like terms: 0 + 51.5 = 51.5 -2x + x2 = 51.5 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 = 51.5 + 1 Reorder the terms: 1 + -2x + x2 = 51.5 + 1 Combine like terms: 51.5 + 1 = 52.5 1 + -2x + x2 = 52.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 52.5 Calculate the square root of the right side: 7.245688373 Break this problem into two subproblems by setting (x + -1) equal to 7.245688373 and -7.245688373.Subproblem 1
x + -1 = 7.245688373 Simplifying x + -1 = 7.245688373 Reorder the terms: -1 + x = 7.245688373 Solving -1 + x = 7.245688373 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 = 7.245688373 + 1 Combine like terms: -1 + 1 = 0 0 + x = 7.245688373 + 1 x = 7.245688373 + 1 Combine like terms: 7.245688373 + 1 = 8.245688373 x = 8.245688373 Simplifying x = 8.245688373Subproblem 2
x + -1 = -7.245688373 Simplifying x + -1 = -7.245688373 Reorder the terms: -1 + x = -7.245688373 Solving -1 + x = -7.245688373 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 = -7.245688373 + 1 Combine like terms: -1 + 1 = 0 0 + x = -7.245688373 + 1 x = -7.245688373 + 1 Combine like terms: -7.245688373 + 1 = -6.245688373 x = -6.245688373 Simplifying x = -6.245688373Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.245688373, -6.245688373}
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