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Simplifying 0 = -16x2 + 3x + 1.3 Reorder the terms: 0 = 1.3 + 3x + -16x2 Solving 0 = 1.3 + 3x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -1.3 = -1.3 -1.3 + -3x + 16x2 = 1.3 + 3x + -16x2 + -1.3 + -3x + 16x2 Reorder the terms: -1.3 + -3x + 16x2 = 1.3 + -1.3 + 3x + -3x + -16x2 + 16x2 Combine like terms: 1.3 + -1.3 = 0.0 -1.3 + -3x + 16x2 = 0.0 + 3x + -3x + -16x2 + 16x2 -1.3 + -3x + 16x2 = 3x + -3x + -16x2 + 16x2 Combine like terms: 3x + -3x = 0 -1.3 + -3x + 16x2 = 0 + -16x2 + 16x2 -1.3 + -3x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -1.3 + -3x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.08125 + -0.1875x + x2 = 0 Move the constant term to the right: Add '0.08125' to each side of the equation. -0.08125 + -0.1875x + 0.08125 + x2 = 0 + 0.08125 Reorder the terms: -0.08125 + 0.08125 + -0.1875x + x2 = 0 + 0.08125 Combine like terms: -0.08125 + 0.08125 = 0.00000 0.00000 + -0.1875x + x2 = 0 + 0.08125 -0.1875x + x2 = 0 + 0.08125 Combine like terms: 0 + 0.08125 = 0.08125 -0.1875x + x2 = 0.08125 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 = 0.08125 + 0.0087890625 Reorder the terms: 0.0087890625 + -0.1875x + x2 = 0.08125 + 0.0087890625 Combine like terms: 0.08125 + 0.0087890625 = 0.0900390625 0.0087890625 + -0.1875x + x2 = 0.0900390625 Factor a perfect square on the left side: (x + -0.09375)(x + -0.09375) = 0.0900390625 Calculate the square root of the right side: 0.300065097 Break this problem into two subproblems by setting (x + -0.09375) equal to 0.300065097 and -0.300065097.Subproblem 1
x + -0.09375 = 0.300065097 Simplifying x + -0.09375 = 0.300065097 Reorder the terms: -0.09375 + x = 0.300065097 Solving -0.09375 + x = 0.300065097 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 = 0.300065097 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + x = 0.300065097 + 0.09375 x = 0.300065097 + 0.09375 Combine like terms: 0.300065097 + 0.09375 = 0.393815097 x = 0.393815097 Simplifying x = 0.393815097Subproblem 2
x + -0.09375 = -0.300065097 Simplifying x + -0.09375 = -0.300065097 Reorder the terms: -0.09375 + x = -0.300065097 Solving -0.09375 + x = -0.300065097 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 = -0.300065097 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + x = -0.300065097 + 0.09375 x = -0.300065097 + 0.09375 Combine like terms: -0.300065097 + 0.09375 = -0.206315097 x = -0.206315097 Simplifying x = -0.206315097Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.393815097, -0.206315097}
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