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Simplifying 64x2 + 48x + -1 = 0 Reorder the terms: -1 + 48x + 64x2 = 0 Solving -1 + 48x + 64x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.015625 + 0.75x + x2 = 0 Move the constant term to the right: Add '0.015625' to each side of the equation. -0.015625 + 0.75x + 0.015625 + x2 = 0 + 0.015625 Reorder the terms: -0.015625 + 0.015625 + 0.75x + x2 = 0 + 0.015625 Combine like terms: -0.015625 + 0.015625 = 0.000000 0.000000 + 0.75x + x2 = 0 + 0.015625 0.75x + x2 = 0 + 0.015625 Combine like terms: 0 + 0.015625 = 0.015625 0.75x + x2 = 0.015625 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 = 0.015625 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 0.015625 + 0.140625 Combine like terms: 0.015625 + 0.140625 = 0.15625 0.140625 + 0.75x + x2 = 0.15625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 0.15625 Calculate the square root of the right side: 0.395284708 Break this problem into two subproblems by setting (x + 0.375) equal to 0.395284708 and -0.395284708.Subproblem 1
x + 0.375 = 0.395284708 Simplifying x + 0.375 = 0.395284708 Reorder the terms: 0.375 + x = 0.395284708 Solving 0.375 + x = 0.395284708 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 = 0.395284708 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 0.395284708 + -0.375 x = 0.395284708 + -0.375 Combine like terms: 0.395284708 + -0.375 = 0.020284708 x = 0.020284708 Simplifying x = 0.020284708Subproblem 2
x + 0.375 = -0.395284708 Simplifying x + 0.375 = -0.395284708 Reorder the terms: 0.375 + x = -0.395284708 Solving 0.375 + x = -0.395284708 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 = -0.395284708 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -0.395284708 + -0.375 x = -0.395284708 + -0.375 Combine like terms: -0.395284708 + -0.375 = -0.770284708 x = -0.770284708 Simplifying x = -0.770284708Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.020284708, -0.770284708}
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