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Simplifying 16x2 + 12x + -3 = 0 Reorder the terms: -3 + 12x + 16x2 = 0 Solving -3 + 12x + 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 + 0.75x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + 0.75x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + 0.75x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + 0.75x + x2 = 0 + 0.1875 0.75x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 0.75x + x2 = 0.1875 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 0.1875 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 0.1875 + 0.140625 Combine like terms: 0.1875 + 0.140625 = 0.328125 0.140625 + 0.75x + x2 = 0.328125 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 0.328125 Calculate the square root of the right side: 0.572821962 Break this problem into two subproblems by setting (x + 0.375) equal to 0.572821962 and -0.572821962.Subproblem 1
x + 0.375 = 0.572821962 Simplifying x + 0.375 = 0.572821962 Reorder the terms: 0.375 + x = 0.572821962 Solving 0.375 + x = 0.572821962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 0.572821962 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 0.572821962 + -0.375 x = 0.572821962 + -0.375 Combine like terms: 0.572821962 + -0.375 = 0.197821962 x = 0.197821962 Simplifying x = 0.197821962Subproblem 2
x + 0.375 = -0.572821962 Simplifying x + 0.375 = -0.572821962 Reorder the terms: 0.375 + x = -0.572821962 Solving 0.375 + x = -0.572821962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -0.572821962 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -0.572821962 + -0.375 x = -0.572821962 + -0.375 Combine like terms: -0.572821962 + -0.375 = -0.947821962 x = -0.947821962 Simplifying x = -0.947821962Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.197821962, -0.947821962}
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