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Simplifying 0 = x2 + x + -682794 Reorder the terms: 0 = -682794 + x + x2 Solving 0 = -682794 + x + x2 Solving for variable 'x'. Combine like terms: 0 + 682794 = 682794 682794 + -1x + -1x2 = -682794 + x + x2 + 682794 + -1x + -1x2 Reorder the terms: 682794 + -1x + -1x2 = -682794 + 682794 + x + -1x + x2 + -1x2 Combine like terms: -682794 + 682794 = 0 682794 + -1x + -1x2 = 0 + x + -1x + x2 + -1x2 682794 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 682794 + -1x + -1x2 = 0 + x2 + -1x2 682794 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 682794 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -682794 + x + x2 = 0 Move the constant term to the right: Add '682794' to each side of the equation. -682794 + x + 682794 + x2 = 0 + 682794 Reorder the terms: -682794 + 682794 + x + x2 = 0 + 682794 Combine like terms: -682794 + 682794 = 0 0 + x + x2 = 0 + 682794 x + x2 = 0 + 682794 Combine like terms: 0 + 682794 = 682794 x + x2 = 682794 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. + 0.25 + x2 = 682794 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 682794 + 0.25 Combine like terms: 682794 + 0.25 = 682794.25 1.25 + x2 = 682794.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 682794.25 Calculate the square root of the right side: 826.313651104 Break this problem into two subproblems by setting (x + 0.5) equal to 826.313651104 and -826.313651104.Subproblem 1
x + 0.5 = 826.313651104 Simplifying x + 0.5 = 826.313651104 Reorder the terms: 0.5 + x = 826.313651104 Solving 0.5 + x = 826.313651104 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 = 826.313651104 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 826.313651104 + -0.5 x = 826.313651104 + -0.5 Combine like terms: 826.313651104 + -0.5 = 825.813651104 x = 825.813651104 Simplifying x = 825.813651104Subproblem 2
x + 0.5 = -826.313651104 Simplifying x + 0.5 = -826.313651104 Reorder the terms: 0.5 + x = -826.313651104 Solving 0.5 + x = -826.313651104 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 = -826.313651104 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -826.313651104 + -0.5 x = -826.313651104 + -0.5 Combine like terms: -826.313651104 + -0.5 = -826.813651104 x = -826.813651104 Simplifying x = -826.813651104Solution
The solution to the problem is based on the solutions from the subproblems. x = {825.813651104, -826.813651104}
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