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Simplifying 1000x2 + 333x + -716 = 0 Reorder the terms: -716 + 333x + 1000x2 = 0 Solving -716 + 333x + 1000x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1000 the coefficient of the squared term: Divide each side by '1000'. -0.716 + 0.333x + x2 = 0 Move the constant term to the right: Add '0.716' to each side of the equation. -0.716 + 0.333x + 0.716 + x2 = 0 + 0.716 Reorder the terms: -0.716 + 0.716 + 0.333x + x2 = 0 + 0.716 Combine like terms: -0.716 + 0.716 = 0.000 0.000 + 0.333x + x2 = 0 + 0.716 0.333x + x2 = 0 + 0.716 Combine like terms: 0 + 0.716 = 0.716 0.333x + x2 = 0.716 The x term is 0.333x. Take half its coefficient (0.1665). Square it (0.02772225) and add it to both sides. Add '0.02772225' to each side of the equation. 0.333x + 0.02772225 + x2 = 0.716 + 0.02772225 Reorder the terms: 0.02772225 + 0.333x + x2 = 0.716 + 0.02772225 Combine like terms: 0.716 + 0.02772225 = 0.74372225 0.02772225 + 0.333x + x2 = 0.74372225 Factor a perfect square on the left side: (x + 0.1665)(x + 0.1665) = 0.74372225 Calculate the square root of the right side: 0.862393327 Break this problem into two subproblems by setting (x + 0.1665) equal to 0.862393327 and -0.862393327.Subproblem 1
x + 0.1665 = 0.862393327 Simplifying x + 0.1665 = 0.862393327 Reorder the terms: 0.1665 + x = 0.862393327 Solving 0.1665 + x = 0.862393327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1665' to each side of the equation. 0.1665 + -0.1665 + x = 0.862393327 + -0.1665 Combine like terms: 0.1665 + -0.1665 = 0.0000 0.0000 + x = 0.862393327 + -0.1665 x = 0.862393327 + -0.1665 Combine like terms: 0.862393327 + -0.1665 = 0.695893327 x = 0.695893327 Simplifying x = 0.695893327Subproblem 2
x + 0.1665 = -0.862393327 Simplifying x + 0.1665 = -0.862393327 Reorder the terms: 0.1665 + x = -0.862393327 Solving 0.1665 + x = -0.862393327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1665' to each side of the equation. 0.1665 + -0.1665 + x = -0.862393327 + -0.1665 Combine like terms: 0.1665 + -0.1665 = 0.0000 0.0000 + x = -0.862393327 + -0.1665 x = -0.862393327 + -0.1665 Combine like terms: -0.862393327 + -0.1665 = -1.028893327 x = -1.028893327 Simplifying x = -1.028893327Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.695893327, -1.028893327}
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