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Simplifying (4x + -1.22)(16x + 3) = 0 Reorder the terms: (-1.22 + 4x)(16x + 3) = 0 Reorder the terms: (-1.22 + 4x)(3 + 16x) = 0 Multiply (-1.22 + 4x) * (3 + 16x) (-1.22(3 + 16x) + 4x * (3 + 16x)) = 0 ((3 * -1.22 + 16x * -1.22) + 4x * (3 + 16x)) = 0 ((-3.66 + -19.52x) + 4x * (3 + 16x)) = 0 (-3.66 + -19.52x + (3 * 4x + 16x * 4x)) = 0 (-3.66 + -19.52x + (12x + 64x2)) = 0 Combine like terms: -19.52x + 12x = -7.52x (-3.66 + -7.52x + 64x2) = 0 Solving -3.66 + -7.52x + 64x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.0571875 + -0.1175x + x2 = 0 Move the constant term to the right: Add '0.0571875' to each side of the equation. -0.0571875 + -0.1175x + 0.0571875 + x2 = 0 + 0.0571875 Reorder the terms: -0.0571875 + 0.0571875 + -0.1175x + x2 = 0 + 0.0571875 Combine like terms: -0.0571875 + 0.0571875 = 0.0000000 0.0000000 + -0.1175x + x2 = 0 + 0.0571875 -0.1175x + x2 = 0 + 0.0571875 Combine like terms: 0 + 0.0571875 = 0.0571875 -0.1175x + x2 = 0.0571875 The x term is -0.1175x. Take half its coefficient (-0.05875). Square it (0.0034515625) and add it to both sides. Add '0.0034515625' to each side of the equation. -0.1175x + 0.0034515625 + x2 = 0.0571875 + 0.0034515625 Reorder the terms: 0.0034515625 + -0.1175x + x2 = 0.0571875 + 0.0034515625 Combine like terms: 0.0571875 + 0.0034515625 = 0.0606390625 0.0034515625 + -0.1175x + x2 = 0.0606390625 Factor a perfect square on the left side: (x + -0.05875)(x + -0.05875) = 0.0606390625 Calculate the square root of the right side: 0.24625 Break this problem into two subproblems by setting (x + -0.05875) equal to 0.24625 and -0.24625.Subproblem 1
x + -0.05875 = 0.24625 Simplifying x + -0.05875 = 0.24625 Reorder the terms: -0.05875 + x = 0.24625 Solving -0.05875 + x = 0.24625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05875' to each side of the equation. -0.05875 + 0.05875 + x = 0.24625 + 0.05875 Combine like terms: -0.05875 + 0.05875 = 0.00000 0.00000 + x = 0.24625 + 0.05875 x = 0.24625 + 0.05875 Combine like terms: 0.24625 + 0.05875 = 0.305 x = 0.305 Simplifying x = 0.305Subproblem 2
x + -0.05875 = -0.24625 Simplifying x + -0.05875 = -0.24625 Reorder the terms: -0.05875 + x = -0.24625 Solving -0.05875 + x = -0.24625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05875' to each side of the equation. -0.05875 + 0.05875 + x = -0.24625 + 0.05875 Combine like terms: -0.05875 + 0.05875 = 0.00000 0.00000 + x = -0.24625 + 0.05875 x = -0.24625 + 0.05875 Combine like terms: -0.24625 + 0.05875 = -0.1875 x = -0.1875 Simplifying x = -0.1875Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.305, -0.1875}
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