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Simplifying 48x2 + 42x + -11 = 0 Reorder the terms: -11 + 42x + 48x2 = 0 Solving -11 + 42x + 48x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.2291666667 + 0.875x + x2 = 0 Move the constant term to the right: Add '0.2291666667' to each side of the equation. -0.2291666667 + 0.875x + 0.2291666667 + x2 = 0 + 0.2291666667 Reorder the terms: -0.2291666667 + 0.2291666667 + 0.875x + x2 = 0 + 0.2291666667 Combine like terms: -0.2291666667 + 0.2291666667 = 0.0000000000 0.0000000000 + 0.875x + x2 = 0 + 0.2291666667 0.875x + x2 = 0 + 0.2291666667 Combine like terms: 0 + 0.2291666667 = 0.2291666667 0.875x + x2 = 0.2291666667 The x term is 0.875x. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875x + 0.19140625 + x2 = 0.2291666667 + 0.19140625 Reorder the terms: 0.19140625 + 0.875x + x2 = 0.2291666667 + 0.19140625 Combine like terms: 0.2291666667 + 0.19140625 = 0.4205729167 0.19140625 + 0.875x + x2 = 0.4205729167 Factor a perfect square on the left side: (x + 0.4375)(x + 0.4375) = 0.4205729167 Calculate the square root of the right side: 0.648515934 Break this problem into two subproblems by setting (x + 0.4375) equal to 0.648515934 and -0.648515934.Subproblem 1
x + 0.4375 = 0.648515934 Simplifying x + 0.4375 = 0.648515934 Reorder the terms: 0.4375 + x = 0.648515934 Solving 0.4375 + x = 0.648515934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = 0.648515934 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = 0.648515934 + -0.4375 x = 0.648515934 + -0.4375 Combine like terms: 0.648515934 + -0.4375 = 0.211015934 x = 0.211015934 Simplifying x = 0.211015934Subproblem 2
x + 0.4375 = -0.648515934 Simplifying x + 0.4375 = -0.648515934 Reorder the terms: 0.4375 + x = -0.648515934 Solving 0.4375 + x = -0.648515934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = -0.648515934 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = -0.648515934 + -0.4375 x = -0.648515934 + -0.4375 Combine like terms: -0.648515934 + -0.4375 = -1.086015934 x = -1.086015934 Simplifying x = -1.086015934Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.211015934, -1.086015934}
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