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Simplifying (5x2 + 8x + -1) + (2x2 + 1x + -2) = 0 Reorder the terms: (-1 + 8x + 5x2) + (2x2 + 1x + -2) = 0 Remove parenthesis around (-1 + 8x + 5x2) -1 + 8x + 5x2 + (2x2 + 1x + -2) = 0 Reorder the terms: -1 + 8x + 5x2 + (-2 + 1x + 2x2) = 0 Remove parenthesis around (-2 + 1x + 2x2) -1 + 8x + 5x2 + -2 + 1x + 2x2 = 0 Reorder the terms: -1 + -2 + 8x + 1x + 5x2 + 2x2 = 0 Combine like terms: -1 + -2 = -3 -3 + 8x + 1x + 5x2 + 2x2 = 0 Combine like terms: 8x + 1x = 9x -3 + 9x + 5x2 + 2x2 = 0 Combine like terms: 5x2 + 2x2 = 7x2 -3 + 9x + 7x2 = 0 Solving -3 + 9x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + 1.285714286x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 1.285714286x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 1.285714286x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 1.285714286x + x2 = 0 + 0.4285714286 1.285714286x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 1.285714286x + x2 = 0.4285714286 The x term is 1.285714286x. Take half its coefficient (0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. 1.285714286x + 0.4132653063 + x2 = 0.4285714286 + 0.4132653063 Reorder the terms: 0.4132653063 + 1.285714286x + x2 = 0.4285714286 + 0.4132653063 Combine like terms: 0.4285714286 + 0.4132653063 = 0.8418367349 0.4132653063 + 1.285714286x + x2 = 0.8418367349 Factor a perfect square on the left side: (x + 0.642857143)(x + 0.642857143) = 0.8418367349 Calculate the square root of the right side: 0.917516613 Break this problem into two subproblems by setting (x + 0.642857143) equal to 0.917516613 and -0.917516613.Subproblem 1
x + 0.642857143 = 0.917516613 Simplifying x + 0.642857143 = 0.917516613 Reorder the terms: 0.642857143 + x = 0.917516613 Solving 0.642857143 + x = 0.917516613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + x = 0.917516613 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = 0.917516613 + -0.642857143 x = 0.917516613 + -0.642857143 Combine like terms: 0.917516613 + -0.642857143 = 0.27465947 x = 0.27465947 Simplifying x = 0.27465947Subproblem 2
x + 0.642857143 = -0.917516613 Simplifying x + 0.642857143 = -0.917516613 Reorder the terms: 0.642857143 + x = -0.917516613 Solving 0.642857143 + x = -0.917516613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + x = -0.917516613 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = -0.917516613 + -0.642857143 x = -0.917516613 + -0.642857143 Combine like terms: -0.917516613 + -0.642857143 = -1.560373756 x = -1.560373756 Simplifying x = -1.560373756Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.27465947, -1.560373756}
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