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Simplifying 0.25x2 + -0.0833x + -0.166 = 0 Reorder the terms: -0.166 + -0.0833x + 0.25x2 = 0 Solving -0.166 + -0.0833x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -0.664 + -0.3332x + x2 = 0 Move the constant term to the right: Add '0.664' to each side of the equation. -0.664 + -0.3332x + 0.664 + x2 = 0 + 0.664 Reorder the terms: -0.664 + 0.664 + -0.3332x + x2 = 0 + 0.664 Combine like terms: -0.664 + 0.664 = 0.000 0.000 + -0.3332x + x2 = 0 + 0.664 -0.3332x + x2 = 0 + 0.664 Combine like terms: 0 + 0.664 = 0.664 -0.3332x + x2 = 0.664 The x term is -0.3332x. Take half its coefficient (-0.1666). Square it (0.02775556) and add it to both sides. Add '0.02775556' to each side of the equation. -0.3332x + 0.02775556 + x2 = 0.664 + 0.02775556 Reorder the terms: 0.02775556 + -0.3332x + x2 = 0.664 + 0.02775556 Combine like terms: 0.664 + 0.02775556 = 0.69175556 0.02775556 + -0.3332x + x2 = 0.69175556 Factor a perfect square on the left side: (x + -0.1666)(x + -0.1666) = 0.69175556 Calculate the square root of the right side: 0.831718438 Break this problem into two subproblems by setting (x + -0.1666) equal to 0.831718438 and -0.831718438.Subproblem 1
x + -0.1666 = 0.831718438 Simplifying x + -0.1666 = 0.831718438 Reorder the terms: -0.1666 + x = 0.831718438 Solving -0.1666 + x = 0.831718438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666' to each side of the equation. -0.1666 + 0.1666 + x = 0.831718438 + 0.1666 Combine like terms: -0.1666 + 0.1666 = 0.0000 0.0000 + x = 0.831718438 + 0.1666 x = 0.831718438 + 0.1666 Combine like terms: 0.831718438 + 0.1666 = 0.998318438 x = 0.998318438 Simplifying x = 0.998318438Subproblem 2
x + -0.1666 = -0.831718438 Simplifying x + -0.1666 = -0.831718438 Reorder the terms: -0.1666 + x = -0.831718438 Solving -0.1666 + x = -0.831718438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666' to each side of the equation. -0.1666 + 0.1666 + x = -0.831718438 + 0.1666 Combine like terms: -0.1666 + 0.1666 = 0.0000 0.0000 + x = -0.831718438 + 0.1666 x = -0.831718438 + 0.1666 Combine like terms: -0.831718438 + 0.1666 = -0.665118438 x = -0.665118438 Simplifying x = -0.665118438Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.998318438, -0.665118438}
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