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Simplifying 16x2 + 3x + -22 = 0 Reorder the terms: -22 + 3x + 16x2 = 0 Solving -22 + 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'. -1.375 + 0.1875x + x2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + 0.1875x + 1.375 + x2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + 0.1875x + x2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + 0.1875x + x2 = 0 + 1.375 0.1875x + x2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 0.1875x + x2 = 1.375 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 = 1.375 + 0.0087890625 Reorder the terms: 0.0087890625 + 0.1875x + x2 = 1.375 + 0.0087890625 Combine like terms: 1.375 + 0.0087890625 = 1.3837890625 0.0087890625 + 0.1875x + x2 = 1.3837890625 Factor a perfect square on the left side: (x + 0.09375)(x + 0.09375) = 1.3837890625 Calculate the square root of the right side: 1.176345639 Break this problem into two subproblems by setting (x + 0.09375) equal to 1.176345639 and -1.176345639.Subproblem 1
x + 0.09375 = 1.176345639 Simplifying x + 0.09375 = 1.176345639 Reorder the terms: 0.09375 + x = 1.176345639 Solving 0.09375 + x = 1.176345639 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 = 1.176345639 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = 1.176345639 + -0.09375 x = 1.176345639 + -0.09375 Combine like terms: 1.176345639 + -0.09375 = 1.082595639 x = 1.082595639 Simplifying x = 1.082595639Subproblem 2
x + 0.09375 = -1.176345639 Simplifying x + 0.09375 = -1.176345639 Reorder the terms: 0.09375 + x = -1.176345639 Solving 0.09375 + x = -1.176345639 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 = -1.176345639 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = -1.176345639 + -0.09375 x = -1.176345639 + -0.09375 Combine like terms: -1.176345639 + -0.09375 = -1.270095639 x = -1.270095639 Simplifying x = -1.270095639Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.082595639, -1.270095639}
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