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Simplifying 28x + -4 = -49x2 Reorder the terms: -4 + 28x = -49x2 Solving -4 + 28x = -49x2 Solving for variable 'x'. Combine like terms: -49x2 + 49x2 = 0 -4 + 28x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.08163265306 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.08163265306' to each side of the equation. -0.08163265306 + 0.5714285714x + 0.08163265306 + x2 = 0 + 0.08163265306 Reorder the terms: -0.08163265306 + 0.08163265306 + 0.5714285714x + x2 = 0 + 0.08163265306 Combine like terms: -0.08163265306 + 0.08163265306 = 0.00000000000 0.00000000000 + 0.5714285714x + x2 = 0 + 0.08163265306 0.5714285714x + x2 = 0 + 0.08163265306 Combine like terms: 0 + 0.08163265306 = 0.08163265306 0.5714285714x + x2 = 0.08163265306 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = 0.08163265306 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 0.08163265306 + 0.08163265305 Combine like terms: 0.08163265306 + 0.08163265305 = 0.16326530611 0.08163265305 + 0.5714285714x + x2 = 0.16326530611 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 0.16326530611 Calculate the square root of the right side: 0.404061018 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 0.404061018 and -0.404061018.Subproblem 1
x + 0.2857142857 = 0.404061018 Simplifying x + 0.2857142857 = 0.404061018 Reorder the terms: 0.2857142857 + x = 0.404061018 Solving 0.2857142857 + x = 0.404061018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 0.404061018 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 0.404061018 + -0.2857142857 x = 0.404061018 + -0.2857142857 Combine like terms: 0.404061018 + -0.2857142857 = 0.1183467323 x = 0.1183467323 Simplifying x = 0.1183467323Subproblem 2
x + 0.2857142857 = -0.404061018 Simplifying x + 0.2857142857 = -0.404061018 Reorder the terms: 0.2857142857 + x = -0.404061018 Solving 0.2857142857 + x = -0.404061018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -0.404061018 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -0.404061018 + -0.2857142857 x = -0.404061018 + -0.2857142857 Combine like terms: -0.404061018 + -0.2857142857 = -0.6897753037 x = -0.6897753037 Simplifying x = -0.6897753037Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1183467323, -0.6897753037}
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