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Simplifying -16x2 + 21x + 6 = 0 Reorder the terms: 6 + 21x + -16x2 = 0 Solving 6 + 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'. -0.375 + -1.3125x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -1.3125x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -1.3125x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -1.3125x + x2 = 0 + 0.375 -1.3125x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -1.3125x + x2 = 0.375 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 = 0.375 + 0.4306640625 Reorder the terms: 0.4306640625 + -1.3125x + x2 = 0.375 + 0.4306640625 Combine like terms: 0.375 + 0.4306640625 = 0.8056640625 0.4306640625 + -1.3125x + x2 = 0.8056640625 Factor a perfect square on the left side: (x + -0.65625)(x + -0.65625) = 0.8056640625 Calculate the square root of the right side: 0.897587914 Break this problem into two subproblems by setting (x + -0.65625) equal to 0.897587914 and -0.897587914.Subproblem 1
x + -0.65625 = 0.897587914 Simplifying x + -0.65625 = 0.897587914 Reorder the terms: -0.65625 + x = 0.897587914 Solving -0.65625 + x = 0.897587914 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 = 0.897587914 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + x = 0.897587914 + 0.65625 x = 0.897587914 + 0.65625 Combine like terms: 0.897587914 + 0.65625 = 1.553837914 x = 1.553837914 Simplifying x = 1.553837914Subproblem 2
x + -0.65625 = -0.897587914 Simplifying x + -0.65625 = -0.897587914 Reorder the terms: -0.65625 + x = -0.897587914 Solving -0.65625 + x = -0.897587914 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 = -0.897587914 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + x = -0.897587914 + 0.65625 x = -0.897587914 + 0.65625 Combine like terms: -0.897587914 + 0.65625 = -0.241337914 x = -0.241337914 Simplifying x = -0.241337914Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.553837914, -0.241337914}
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