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Simplifying 0.25x2 + 0.666x + -0.5 = 0 Reorder the terms: -0.5 + 0.666x + 0.25x2 = 0 Solving -0.5 + 0.666x + 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'. -2 + 2.664x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 2.664x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 2.664x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2.664x + x2 = 0 + 2 2.664x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 2.664x + x2 = 2 The x term is 2.664x. Take half its coefficient (1.332). Square it (1.774224) and add it to both sides. Add '1.774224' to each side of the equation. 2.664x + 1.774224 + x2 = 2 + 1.774224 Reorder the terms: 1.774224 + 2.664x + x2 = 2 + 1.774224 Combine like terms: 2 + 1.774224 = 3.774224 1.774224 + 2.664x + x2 = 3.774224 Factor a perfect square on the left side: (x + 1.332)(x + 1.332) = 3.774224 Calculate the square root of the right side: 1.942736215 Break this problem into two subproblems by setting (x + 1.332) equal to 1.942736215 and -1.942736215.Subproblem 1
x + 1.332 = 1.942736215 Simplifying x + 1.332 = 1.942736215 Reorder the terms: 1.332 + x = 1.942736215 Solving 1.332 + x = 1.942736215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.332' to each side of the equation. 1.332 + -1.332 + x = 1.942736215 + -1.332 Combine like terms: 1.332 + -1.332 = 0.000 0.000 + x = 1.942736215 + -1.332 x = 1.942736215 + -1.332 Combine like terms: 1.942736215 + -1.332 = 0.610736215 x = 0.610736215 Simplifying x = 0.610736215Subproblem 2
x + 1.332 = -1.942736215 Simplifying x + 1.332 = -1.942736215 Reorder the terms: 1.332 + x = -1.942736215 Solving 1.332 + x = -1.942736215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.332' to each side of the equation. 1.332 + -1.332 + x = -1.942736215 + -1.332 Combine like terms: 1.332 + -1.332 = 0.000 0.000 + x = -1.942736215 + -1.332 x = -1.942736215 + -1.332 Combine like terms: -1.942736215 + -1.332 = -3.274736215 x = -3.274736215 Simplifying x = -3.274736215Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.610736215, -3.274736215}
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