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Simplifying 16x2 + -3x + -5 = 0 Reorder the terms: -5 + -3x + 16x2 = 0 Solving -5 + -3x + 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'. -0.3125 + -0.1875x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -0.1875x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -0.1875x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -0.1875x + x2 = 0 + 0.3125 -0.1875x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -0.1875x + x2 = 0.3125 The x term is -0.1875x. Take half its coefficient (-0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. -0.1875x + 0.0087890625 + x2 = 0.3125 + 0.0087890625 Reorder the terms: 0.0087890625 + -0.1875x + x2 = 0.3125 + 0.0087890625 Combine like terms: 0.3125 + 0.0087890625 = 0.3212890625 0.0087890625 + -0.1875x + x2 = 0.3212890625 Factor a perfect square on the left side: (x + -0.09375)(x + -0.09375) = 0.3212890625 Calculate the square root of the right side: 0.566823661 Break this problem into two subproblems by setting (x + -0.09375) equal to 0.566823661 and -0.566823661.Subproblem 1
x + -0.09375 = 0.566823661 Simplifying x + -0.09375 = 0.566823661 Reorder the terms: -0.09375 + x = 0.566823661 Solving -0.09375 + x = 0.566823661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + x = 0.566823661 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + x = 0.566823661 + 0.09375 x = 0.566823661 + 0.09375 Combine like terms: 0.566823661 + 0.09375 = 0.660573661 x = 0.660573661 Simplifying x = 0.660573661Subproblem 2
x + -0.09375 = -0.566823661 Simplifying x + -0.09375 = -0.566823661 Reorder the terms: -0.09375 + x = -0.566823661 Solving -0.09375 + x = -0.566823661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + x = -0.566823661 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + x = -0.566823661 + 0.09375 x = -0.566823661 + 0.09375 Combine like terms: -0.566823661 + 0.09375 = -0.473073661 x = -0.473073661 Simplifying x = -0.473073661Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.660573661, -0.473073661}
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