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Simplifying x2 + -105x + 731 = 0 Reorder the terms: 731 + -105x + x2 = 0 Solving 731 + -105x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-731' to each side of the equation. 731 + -105x + -731 + x2 = 0 + -731 Reorder the terms: 731 + -731 + -105x + x2 = 0 + -731 Combine like terms: 731 + -731 = 0 0 + -105x + x2 = 0 + -731 -105x + x2 = 0 + -731 Combine like terms: 0 + -731 = -731 -105x + x2 = -731 The x term is -105x. Take half its coefficient (-52.5). Square it (2756.25) and add it to both sides. Add '2756.25' to each side of the equation. -105x + 2756.25 + x2 = -731 + 2756.25 Reorder the terms: 2756.25 + -105x + x2 = -731 + 2756.25 Combine like terms: -731 + 2756.25 = 2025.25 2756.25 + -105x + x2 = 2025.25 Factor a perfect square on the left side: (x + -52.5)(x + -52.5) = 2025.25 Calculate the square root of the right side: 45.002777692 Break this problem into two subproblems by setting (x + -52.5) equal to 45.002777692 and -45.002777692.Subproblem 1
x + -52.5 = 45.002777692 Simplifying x + -52.5 = 45.002777692 Reorder the terms: -52.5 + x = 45.002777692 Solving -52.5 + x = 45.002777692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52.5' to each side of the equation. -52.5 + 52.5 + x = 45.002777692 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + x = 45.002777692 + 52.5 x = 45.002777692 + 52.5 Combine like terms: 45.002777692 + 52.5 = 97.502777692 x = 97.502777692 Simplifying x = 97.502777692Subproblem 2
x + -52.5 = -45.002777692 Simplifying x + -52.5 = -45.002777692 Reorder the terms: -52.5 + x = -45.002777692 Solving -52.5 + x = -45.002777692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52.5' to each side of the equation. -52.5 + 52.5 + x = -45.002777692 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + x = -45.002777692 + 52.5 x = -45.002777692 + 52.5 Combine like terms: -45.002777692 + 52.5 = 7.497222308 x = 7.497222308 Simplifying x = 7.497222308Solution
The solution to the problem is based on the solutions from the subproblems. x = {97.502777692, 7.497222308}
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