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Simplifying (16x2) + -21x + 3 = 0 Reorder the terms: 3 + -21x + (16x2) = 0 Solving 3 + -21x + (16x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.1875 + -1.3125x + x2 = 0 Move the constant term to the right: Add '-0.1875' to each side of the equation. 0.1875 + -1.3125x + -0.1875 + x2 = 0 + -0.1875 Reorder the terms: 0.1875 + -0.1875 + -1.3125x + x2 = 0 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + -1.3125x + x2 = 0 + -0.1875 -1.3125x + x2 = 0 + -0.1875 Combine like terms: 0 + -0.1875 = -0.1875 -1.3125x + x2 = -0.1875 The x term is -1.3125x. Take half its coefficient (-0.65625). Square it (0.4306640625) and add it to both sides. Add '0.4306640625' to each side of the equation. -1.3125x + 0.4306640625 + x2 = -0.1875 + 0.4306640625 Reorder the terms: 0.4306640625 + -1.3125x + x2 = -0.1875 + 0.4306640625 Combine like terms: -0.1875 + 0.4306640625 = 0.2431640625 0.4306640625 + -1.3125x + x2 = 0.2431640625 Factor a perfect square on the left side: ((x) + -0.65625)((x) + -0.65625) = 0.2431640625 Calculate the square root of the right side: 0.493116682 Break this problem into two subproblems by setting ((x) + -0.65625) equal to 0.493116682 and -0.493116682.Subproblem 1
(x) + -0.65625 = 0.493116682 Simplifying (x) + -0.65625 = 0.493116682 x + -0.65625 = 0.493116682 Reorder the terms: -0.65625 + x = 0.493116682 Solving -0.65625 + x = 0.493116682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65625' to each side of the equation. -0.65625 + 0.65625 + x = 0.493116682 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + x = 0.493116682 + 0.65625 x = 0.493116682 + 0.65625 Combine like terms: 0.493116682 + 0.65625 = 1.149366682 x = 1.149366682 Simplifying x = 1.149366682Subproblem 2
(x) + -0.65625 = -0.493116682 Simplifying (x) + -0.65625 = -0.493116682 x + -0.65625 = -0.493116682 Reorder the terms: -0.65625 + x = -0.493116682 Solving -0.65625 + x = -0.493116682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65625' to each side of the equation. -0.65625 + 0.65625 + x = -0.493116682 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + x = -0.493116682 + 0.65625 x = -0.493116682 + 0.65625 Combine like terms: -0.493116682 + 0.65625 = 0.163133318 x = 0.163133318 Simplifying x = 0.163133318Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.149366682, 0.163133318}
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