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Simplifying 2x2 + 47x + -63 = 0 Reorder the terms: -63 + 47x + 2x2 = 0 Solving -63 + 47x + 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'. -31.5 + 23.5x + x2 = 0 Move the constant term to the right: Add '31.5' to each side of the equation. -31.5 + 23.5x + 31.5 + x2 = 0 + 31.5 Reorder the terms: -31.5 + 31.5 + 23.5x + x2 = 0 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + 23.5x + x2 = 0 + 31.5 23.5x + x2 = 0 + 31.5 Combine like terms: 0 + 31.5 = 31.5 23.5x + x2 = 31.5 The x term is 23.5x. Take half its coefficient (11.75). Square it (138.0625) and add it to both sides. Add '138.0625' to each side of the equation. 23.5x + 138.0625 + x2 = 31.5 + 138.0625 Reorder the terms: 138.0625 + 23.5x + x2 = 31.5 + 138.0625 Combine like terms: 31.5 + 138.0625 = 169.5625 138.0625 + 23.5x + x2 = 169.5625 Factor a perfect square on the left side: (x + 11.75)(x + 11.75) = 169.5625 Calculate the square root of the right side: 13.021616643 Break this problem into two subproblems by setting (x + 11.75) equal to 13.021616643 and -13.021616643.Subproblem 1
x + 11.75 = 13.021616643 Simplifying x + 11.75 = 13.021616643 Reorder the terms: 11.75 + x = 13.021616643 Solving 11.75 + x = 13.021616643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.75' to each side of the equation. 11.75 + -11.75 + x = 13.021616643 + -11.75 Combine like terms: 11.75 + -11.75 = 0.00 0.00 + x = 13.021616643 + -11.75 x = 13.021616643 + -11.75 Combine like terms: 13.021616643 + -11.75 = 1.271616643 x = 1.271616643 Simplifying x = 1.271616643Subproblem 2
x + 11.75 = -13.021616643 Simplifying x + 11.75 = -13.021616643 Reorder the terms: 11.75 + x = -13.021616643 Solving 11.75 + x = -13.021616643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.75' to each side of the equation. 11.75 + -11.75 + x = -13.021616643 + -11.75 Combine like terms: 11.75 + -11.75 = 0.00 0.00 + x = -13.021616643 + -11.75 x = -13.021616643 + -11.75 Combine like terms: -13.021616643 + -11.75 = -24.771616643 x = -24.771616643 Simplifying x = -24.771616643Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.271616643, -24.771616643}
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