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Simplifying 2x2 + -20x + 37 = 0 Reorder the terms: 37 + -20x + 2x2 = 0 Solving 37 + -20x + 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'. 18.5 + -10x + x2 = 0 Move the constant term to the right: Add '-18.5' to each side of the equation. 18.5 + -10x + -18.5 + x2 = 0 + -18.5 Reorder the terms: 18.5 + -18.5 + -10x + x2 = 0 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + -10x + x2 = 0 + -18.5 -10x + x2 = 0 + -18.5 Combine like terms: 0 + -18.5 = -18.5 -10x + x2 = -18.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -18.5 + 25 Reorder the terms: 25 + -10x + x2 = -18.5 + 25 Combine like terms: -18.5 + 25 = 6.5 25 + -10x + x2 = 6.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (x + -5) equal to 2.549509757 and -2.549509757.Subproblem 1
x + -5 = 2.549509757 Simplifying x + -5 = 2.549509757 Reorder the terms: -5 + x = 2.549509757 Solving -5 + x = 2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 2.549509757 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.549509757 + 5 x = 2.549509757 + 5 Combine like terms: 2.549509757 + 5 = 7.549509757 x = 7.549509757 Simplifying x = 7.549509757Subproblem 2
x + -5 = -2.549509757 Simplifying x + -5 = -2.549509757 Reorder the terms: -5 + x = -2.549509757 Solving -5 + x = -2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -2.549509757 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.549509757 + 5 x = -2.549509757 + 5 Combine like terms: -2.549509757 + 5 = 2.450490243 x = 2.450490243 Simplifying x = 2.450490243Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.549509757, 2.450490243}
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