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Simplifying -16x2 + 332x + 6 = 0 Reorder the terms: 6 + 332x + -16x2 = 0 Solving 6 + 332x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 166x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 166x + -8x2)' equal to zero and attempt to solve: Simplifying 3 + 166x + -8x2 = 0 Solving 3 + 166x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + -20.75x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -20.75x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -20.75x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -20.75x + x2 = 0 + 0.375 -20.75x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -20.75x + x2 = 0.375 The x term is -20.75x. Take half its coefficient (-10.375). Square it (107.640625) and add it to both sides. Add '107.640625' to each side of the equation. -20.75x + 107.640625 + x2 = 0.375 + 107.640625 Reorder the terms: 107.640625 + -20.75x + x2 = 0.375 + 107.640625 Combine like terms: 0.375 + 107.640625 = 108.015625 107.640625 + -20.75x + x2 = 108.015625 Factor a perfect square on the left side: (x + -10.375)(x + -10.375) = 108.015625 Calculate the square root of the right side: 10.393056576 Break this problem into two subproblems by setting (x + -10.375) equal to 10.393056576 and -10.393056576.Subproblem 1
x + -10.375 = 10.393056576 Simplifying x + -10.375 = 10.393056576 Reorder the terms: -10.375 + x = 10.393056576 Solving -10.375 + x = 10.393056576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.375' to each side of the equation. -10.375 + 10.375 + x = 10.393056576 + 10.375 Combine like terms: -10.375 + 10.375 = 0.000 0.000 + x = 10.393056576 + 10.375 x = 10.393056576 + 10.375 Combine like terms: 10.393056576 + 10.375 = 20.768056576 x = 20.768056576 Simplifying x = 20.768056576Subproblem 2
x + -10.375 = -10.393056576 Simplifying x + -10.375 = -10.393056576 Reorder the terms: -10.375 + x = -10.393056576 Solving -10.375 + x = -10.393056576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.375' to each side of the equation. -10.375 + 10.375 + x = -10.393056576 + 10.375 Combine like terms: -10.375 + 10.375 = 0.000 0.000 + x = -10.393056576 + 10.375 x = -10.393056576 + 10.375 Combine like terms: -10.393056576 + 10.375 = -0.018056576 x = -0.018056576 Simplifying x = -0.018056576Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.768056576, -0.018056576}Solution
x = {20.768056576, -0.018056576}
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