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Simplifying -16x2 + 5.5x + 10 = 0 Reorder the terms: 10 + 5.5x + -16x2 = 0 Solving 10 + 5.5x + -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'. -0.625 + -0.34375x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -0.34375x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -0.34375x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -0.34375x + x2 = 0 + 0.625 -0.34375x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -0.34375x + x2 = 0.625 The x term is -0.34375x. Take half its coefficient (-0.171875). Square it (0.02954101563) and add it to both sides. Add '0.02954101563' to each side of the equation. -0.34375x + 0.02954101563 + x2 = 0.625 + 0.02954101563 Reorder the terms: 0.02954101563 + -0.34375x + x2 = 0.625 + 0.02954101563 Combine like terms: 0.625 + 0.02954101563 = 0.65454101563 0.02954101563 + -0.34375x + x2 = 0.65454101563 Factor a perfect square on the left side: (x + -0.171875)(x + -0.171875) = 0.65454101563 Calculate the square root of the right side: 0.809037092 Break this problem into two subproblems by setting (x + -0.171875) equal to 0.809037092 and -0.809037092.Subproblem 1
x + -0.171875 = 0.809037092 Simplifying x + -0.171875 = 0.809037092 Reorder the terms: -0.171875 + x = 0.809037092 Solving -0.171875 + x = 0.809037092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.171875' to each side of the equation. -0.171875 + 0.171875 + x = 0.809037092 + 0.171875 Combine like terms: -0.171875 + 0.171875 = 0.000000 0.000000 + x = 0.809037092 + 0.171875 x = 0.809037092 + 0.171875 Combine like terms: 0.809037092 + 0.171875 = 0.980912092 x = 0.980912092 Simplifying x = 0.980912092Subproblem 2
x + -0.171875 = -0.809037092 Simplifying x + -0.171875 = -0.809037092 Reorder the terms: -0.171875 + x = -0.809037092 Solving -0.171875 + x = -0.809037092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.171875' to each side of the equation. -0.171875 + 0.171875 + x = -0.809037092 + 0.171875 Combine like terms: -0.171875 + 0.171875 = 0.000000 0.000000 + x = -0.809037092 + 0.171875 x = -0.809037092 + 0.171875 Combine like terms: -0.809037092 + 0.171875 = -0.637162092 x = -0.637162092 Simplifying x = -0.637162092Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.980912092, -0.637162092}
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