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Simplifying 880x(880x) + x = 10 Remove parenthesis around (880x) 880x * 880x + x = 10 Reorder the terms for easier multiplication: 880 * 880x * x + x = 10 Multiply 880 * 880 774400x * x + x = 10 Multiply x * x 774400x2 + x = 10 Reorder the terms: x + 774400x2 = 10 Solving x + 774400x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + x + 774400x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + x + 774400x2 = 0 Begin completing the square. Divide all terms by 774400 the coefficient of the squared term: Divide each side by '774400'. -0.00001291322314 + 0.000001291322314x + x2 = 0.00 Move the constant term to the right: Add '0.00001291322314' to each side of the equation. -0.00001291322314 + 0.000001291322314x + 0.00001291322314 + x2 = 0.00 + 0.00001291322314 Reorder the terms: -0.00001291322314 + 0.00001291322314 + 0.000001291322314x + x2 = 0.00 + 0.00001291322314 Combine like terms: -0.00001291322314 + 0.00001291322314 = 0.00000000000000 0.00000000000000 + 0.000001291322314x + x2 = 0.00 + 0.00001291322314 0.000001291322314x + x2 = 0.00 + 0.00001291322314 Combine like terms: 0.00 + 0.00001291322314 = 0.00001291322314 0.000001291322314x + x2 = 0.00001291322314 The x term is x. 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. 0.000001291322314x + 0.25 + x2 = 0.00001291322314 + 0.25 Reorder the terms: 0.25 + 0.000001291322314x + x2 = 0.00001291322314 + 0.25 Combine like terms: 0.00001291322314 + 0.25 = 0.25001291322314 0.25 + 0.000001291322314x + x2 = 0.25001291322314 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.25001291322314 Calculate the square root of the right side: 0.500012913 Break this problem into two subproblems by setting (x + 0.5) equal to 0.500012913 and -0.500012913.Subproblem 1
x + 0.5 = 0.500012913 Simplifying x + 0.5 = 0.500012913 Reorder the terms: 0.5 + x = 0.500012913 Solving 0.5 + x = 0.500012913 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 = 0.500012913 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.500012913 + -0.5 x = 0.500012913 + -0.5 Combine like terms: 0.500012913 + -0.5 = 0.000012913 x = 0.000012913 Simplifying x = 0.000012913Subproblem 2
x + 0.5 = -0.500012913 Simplifying x + 0.5 = -0.500012913 Reorder the terms: 0.5 + x = -0.500012913 Solving 0.5 + x = -0.500012913 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 = -0.500012913 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.500012913 + -0.5 x = -0.500012913 + -0.5 Combine like terms: -0.500012913 + -0.5 = -1.000012913 x = -1.000012913 Simplifying x = -1.000012913Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000012913, -1.000012913}
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