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Simplifying 25x2 + -11x + -6 = 0 Reorder the terms: -6 + -11x + 25x2 = 0 Solving -6 + -11x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.24 + -0.44x + x2 = 0 Move the constant term to the right: Add '0.24' to each side of the equation. -0.24 + -0.44x + 0.24 + x2 = 0 + 0.24 Reorder the terms: -0.24 + 0.24 + -0.44x + x2 = 0 + 0.24 Combine like terms: -0.24 + 0.24 = 0.00 0.00 + -0.44x + x2 = 0 + 0.24 -0.44x + x2 = 0 + 0.24 Combine like terms: 0 + 0.24 = 0.24 -0.44x + x2 = 0.24 The x term is -0.44x. Take half its coefficient (-0.22). Square it (0.0484) and add it to both sides. Add '0.0484' to each side of the equation. -0.44x + 0.0484 + x2 = 0.24 + 0.0484 Reorder the terms: 0.0484 + -0.44x + x2 = 0.24 + 0.0484 Combine like terms: 0.24 + 0.0484 = 0.2884 0.0484 + -0.44x + x2 = 0.2884 Factor a perfect square on the left side: (x + -0.22)(x + -0.22) = 0.2884 Calculate the square root of the right side: 0.537028863 Break this problem into two subproblems by setting (x + -0.22) equal to 0.537028863 and -0.537028863.Subproblem 1
x + -0.22 = 0.537028863 Simplifying x + -0.22 = 0.537028863 Reorder the terms: -0.22 + x = 0.537028863 Solving -0.22 + x = 0.537028863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.22' to each side of the equation. -0.22 + 0.22 + x = 0.537028863 + 0.22 Combine like terms: -0.22 + 0.22 = 0.00 0.00 + x = 0.537028863 + 0.22 x = 0.537028863 + 0.22 Combine like terms: 0.537028863 + 0.22 = 0.757028863 x = 0.757028863 Simplifying x = 0.757028863Subproblem 2
x + -0.22 = -0.537028863 Simplifying x + -0.22 = -0.537028863 Reorder the terms: -0.22 + x = -0.537028863 Solving -0.22 + x = -0.537028863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.22' to each side of the equation. -0.22 + 0.22 + x = -0.537028863 + 0.22 Combine like terms: -0.22 + 0.22 = 0.00 0.00 + x = -0.537028863 + 0.22 x = -0.537028863 + 0.22 Combine like terms: -0.537028863 + 0.22 = -0.317028863 x = -0.317028863 Simplifying x = -0.317028863Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.757028863, -0.317028863}
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