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Simplifying 16x2 + 27x + 6 = 0 Reorder the terms: 6 + 27x + 16x2 = 0 Solving 6 + 27x + 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'. 0.375 + 1.6875x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 1.6875x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 1.6875x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 1.6875x + x2 = 0 + -0.375 1.6875x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 1.6875x + x2 = -0.375 The x term is 1.6875x. Take half its coefficient (0.84375). Square it (0.7119140625) and add it to both sides. Add '0.7119140625' to each side of the equation. 1.6875x + 0.7119140625 + x2 = -0.375 + 0.7119140625 Reorder the terms: 0.7119140625 + 1.6875x + x2 = -0.375 + 0.7119140625 Combine like terms: -0.375 + 0.7119140625 = 0.3369140625 0.7119140625 + 1.6875x + x2 = 0.3369140625 Factor a perfect square on the left side: (x + 0.84375)(x + 0.84375) = 0.3369140625 Calculate the square root of the right side: 0.580442988 Break this problem into two subproblems by setting (x + 0.84375) equal to 0.580442988 and -0.580442988.Subproblem 1
x + 0.84375 = 0.580442988 Simplifying x + 0.84375 = 0.580442988 Reorder the terms: 0.84375 + x = 0.580442988 Solving 0.84375 + x = 0.580442988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.84375' to each side of the equation. 0.84375 + -0.84375 + x = 0.580442988 + -0.84375 Combine like terms: 0.84375 + -0.84375 = 0.00000 0.00000 + x = 0.580442988 + -0.84375 x = 0.580442988 + -0.84375 Combine like terms: 0.580442988 + -0.84375 = -0.263307012 x = -0.263307012 Simplifying x = -0.263307012Subproblem 2
x + 0.84375 = -0.580442988 Simplifying x + 0.84375 = -0.580442988 Reorder the terms: 0.84375 + x = -0.580442988 Solving 0.84375 + x = -0.580442988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.84375' to each side of the equation. 0.84375 + -0.84375 + x = -0.580442988 + -0.84375 Combine like terms: 0.84375 + -0.84375 = 0.00000 0.00000 + x = -0.580442988 + -0.84375 x = -0.580442988 + -0.84375 Combine like terms: -0.580442988 + -0.84375 = -1.424192988 x = -1.424192988 Simplifying x = -1.424192988Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.263307012, -1.424192988}
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