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Simplifying 49x2 + 28x = 22 Reorder the terms: 28x + 49x2 = 22 Solving 28x + 49x2 = 22 Solving for variable 'x'. Reorder the terms: -22 + 28x + 49x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -22 + 28x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.4489795918 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.4489795918' to each side of the equation. -0.4489795918 + 0.5714285714x + 0.4489795918 + x2 = 0 + 0.4489795918 Reorder the terms: -0.4489795918 + 0.4489795918 + 0.5714285714x + x2 = 0 + 0.4489795918 Combine like terms: -0.4489795918 + 0.4489795918 = 0.0000000000 0.0000000000 + 0.5714285714x + x2 = 0 + 0.4489795918 0.5714285714x + x2 = 0 + 0.4489795918 Combine like terms: 0 + 0.4489795918 = 0.4489795918 0.5714285714x + x2 = 0.4489795918 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 = 0.4489795918 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 0.4489795918 + 0.08163265305 Combine like terms: 0.4489795918 + 0.08163265305 = 0.53061224485 0.08163265305 + 0.5714285714x + x2 = 0.53061224485 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 0.53061224485 Calculate the square root of the right side: 0.728431359 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 0.728431359 and -0.728431359.Subproblem 1
x + 0.2857142857 = 0.728431359 Simplifying x + 0.2857142857 = 0.728431359 Reorder the terms: 0.2857142857 + x = 0.728431359 Solving 0.2857142857 + x = 0.728431359 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 = 0.728431359 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 0.728431359 + -0.2857142857 x = 0.728431359 + -0.2857142857 Combine like terms: 0.728431359 + -0.2857142857 = 0.4427170733 x = 0.4427170733 Simplifying x = 0.4427170733Subproblem 2
x + 0.2857142857 = -0.728431359 Simplifying x + 0.2857142857 = -0.728431359 Reorder the terms: 0.2857142857 + x = -0.728431359 Solving 0.2857142857 + x = -0.728431359 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 = -0.728431359 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -0.728431359 + -0.2857142857 x = -0.728431359 + -0.2857142857 Combine like terms: -0.728431359 + -0.2857142857 = -1.0141456447 x = -1.0141456447 Simplifying x = -1.0141456447Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4427170733, -1.0141456447}
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