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Simplifying 16x2 + 3x + -124 = 0 Reorder the terms: -124 + 3x + 16x2 = 0 Solving -124 + 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'. -7.75 + 0.1875x + x2 = 0 Move the constant term to the right: Add '7.75' to each side of the equation. -7.75 + 0.1875x + 7.75 + x2 = 0 + 7.75 Reorder the terms: -7.75 + 7.75 + 0.1875x + x2 = 0 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + 0.1875x + x2 = 0 + 7.75 0.1875x + x2 = 0 + 7.75 Combine like terms: 0 + 7.75 = 7.75 0.1875x + x2 = 7.75 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 = 7.75 + 0.0087890625 Reorder the terms: 0.0087890625 + 0.1875x + x2 = 7.75 + 0.0087890625 Combine like terms: 7.75 + 0.0087890625 = 7.7587890625 0.0087890625 + 0.1875x + x2 = 7.7587890625 Factor a perfect square on the left side: (x + 0.09375)(x + 0.09375) = 7.7587890625 Calculate the square root of the right side: 2.785460296 Break this problem into two subproblems by setting (x + 0.09375) equal to 2.785460296 and -2.785460296.Subproblem 1
x + 0.09375 = 2.785460296 Simplifying x + 0.09375 = 2.785460296 Reorder the terms: 0.09375 + x = 2.785460296 Solving 0.09375 + x = 2.785460296 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 = 2.785460296 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = 2.785460296 + -0.09375 x = 2.785460296 + -0.09375 Combine like terms: 2.785460296 + -0.09375 = 2.691710296 x = 2.691710296 Simplifying x = 2.691710296Subproblem 2
x + 0.09375 = -2.785460296 Simplifying x + 0.09375 = -2.785460296 Reorder the terms: 0.09375 + x = -2.785460296 Solving 0.09375 + x = -2.785460296 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 = -2.785460296 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = -2.785460296 + -0.09375 x = -2.785460296 + -0.09375 Combine like terms: -2.785460296 + -0.09375 = -2.879210296 x = -2.879210296 Simplifying x = -2.879210296Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.691710296, -2.879210296}
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