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Simplifying x2 + -37x + 25 = 34 Reorder the terms: 25 + -37x + x2 = 34 Solving 25 + -37x + x2 = 34 Solving for variable 'x'. Reorder the terms: 25 + -34 + -37x + x2 = 34 + -34 Combine like terms: 25 + -34 = -9 -9 + -37x + x2 = 34 + -34 Combine like terms: 34 + -34 = 0 -9 + -37x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -37x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -37x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -37x + x2 = 0 + 9 -37x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -37x + x2 = 9 The x term is -37x. Take half its coefficient (-18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. -37x + 342.25 + x2 = 9 + 342.25 Reorder the terms: 342.25 + -37x + x2 = 9 + 342.25 Combine like terms: 9 + 342.25 = 351.25 342.25 + -37x + x2 = 351.25 Factor a perfect square on the left side: (x + -18.5)(x + -18.5) = 351.25 Calculate the square root of the right side: 18.741664814 Break this problem into two subproblems by setting (x + -18.5) equal to 18.741664814 and -18.741664814.Subproblem 1
x + -18.5 = 18.741664814 Simplifying x + -18.5 = 18.741664814 Reorder the terms: -18.5 + x = 18.741664814 Solving -18.5 + x = 18.741664814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = 18.741664814 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = 18.741664814 + 18.5 x = 18.741664814 + 18.5 Combine like terms: 18.741664814 + 18.5 = 37.241664814 x = 37.241664814 Simplifying x = 37.241664814Subproblem 2
x + -18.5 = -18.741664814 Simplifying x + -18.5 = -18.741664814 Reorder the terms: -18.5 + x = -18.741664814 Solving -18.5 + x = -18.741664814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = -18.741664814 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = -18.741664814 + 18.5 x = -18.741664814 + 18.5 Combine like terms: -18.741664814 + 18.5 = -0.241664814 x = -0.241664814 Simplifying x = -0.241664814Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.241664814, -0.241664814}
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