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Simplifying x2 + -1x + 10 = 425 Reorder the terms: 10 + -1x + x2 = 425 Solving 10 + -1x + x2 = 425 Solving for variable 'x'. Reorder the terms: 10 + -425 + -1x + x2 = 425 + -425 Combine like terms: 10 + -425 = -415 -415 + -1x + x2 = 425 + -425 Combine like terms: 425 + -425 = 0 -415 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '415' to each side of the equation. -415 + -1x + 415 + x2 = 0 + 415 Reorder the terms: -415 + 415 + -1x + x2 = 0 + 415 Combine like terms: -415 + 415 = 0 0 + -1x + x2 = 0 + 415 -1x + x2 = 0 + 415 Combine like terms: 0 + 415 = 415 -1x + x2 = 415 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 415 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 415 + 0.25 Combine like terms: 415 + 0.25 = 415.25 0.25 + -1x + x2 = 415.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 415.25 Calculate the square root of the right side: 20.377683872 Break this problem into two subproblems by setting (x + -0.5) equal to 20.377683872 and -20.377683872.Subproblem 1
x + -0.5 = 20.377683872 Simplifying x + -0.5 = 20.377683872 Reorder the terms: -0.5 + x = 20.377683872 Solving -0.5 + x = 20.377683872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 20.377683872 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 20.377683872 + 0.5 x = 20.377683872 + 0.5 Combine like terms: 20.377683872 + 0.5 = 20.877683872 x = 20.877683872 Simplifying x = 20.877683872Subproblem 2
x + -0.5 = -20.377683872 Simplifying x + -0.5 = -20.377683872 Reorder the terms: -0.5 + x = -20.377683872 Solving -0.5 + x = -20.377683872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -20.377683872 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -20.377683872 + 0.5 x = -20.377683872 + 0.5 Combine like terms: -20.377683872 + 0.5 = -19.877683872 x = -19.877683872 Simplifying x = -19.877683872Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.877683872, -19.877683872}
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