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Simplifying (7x2 + -5x + 5) + (9x + -10) = 0 Reorder the terms: (5 + -5x + 7x2) + (9x + -10) = 0 Remove parenthesis around (5 + -5x + 7x2) 5 + -5x + 7x2 + (9x + -10) = 0 Reorder the terms: 5 + -5x + 7x2 + (-10 + 9x) = 0 Remove parenthesis around (-10 + 9x) 5 + -5x + 7x2 + -10 + 9x = 0 Reorder the terms: 5 + -10 + -5x + 9x + 7x2 = 0 Combine like terms: 5 + -10 = -5 -5 + -5x + 9x + 7x2 = 0 Combine like terms: -5x + 9x = 4x -5 + 4x + 7x2 = 0 Solving -5 + 4x + 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'. -0.7142857143 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 0.5714285714x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 0.5714285714x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 0.5714285714x + x2 = 0 + 0.7142857143 0.5714285714x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 0.5714285714x + x2 = 0.7142857143 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 = 0.7142857143 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 0.7142857143 + 0.08163265305 Combine like terms: 0.7142857143 + 0.08163265305 = 0.79591836735 0.08163265305 + 0.5714285714x + x2 = 0.79591836735 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 0.79591836735 Calculate the square root of the right side: 0.892142571 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 0.892142571 and -0.892142571.Subproblem 1
x + 0.2857142857 = 0.892142571 Simplifying x + 0.2857142857 = 0.892142571 Reorder the terms: 0.2857142857 + x = 0.892142571 Solving 0.2857142857 + x = 0.892142571 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 = 0.892142571 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 0.892142571 + -0.2857142857 x = 0.892142571 + -0.2857142857 Combine like terms: 0.892142571 + -0.2857142857 = 0.6064282853 x = 0.6064282853 Simplifying x = 0.6064282853Subproblem 2
x + 0.2857142857 = -0.892142571 Simplifying x + 0.2857142857 = -0.892142571 Reorder the terms: 0.2857142857 + x = -0.892142571 Solving 0.2857142857 + x = -0.892142571 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 = -0.892142571 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -0.892142571 + -0.2857142857 x = -0.892142571 + -0.2857142857 Combine like terms: -0.892142571 + -0.2857142857 = -1.1778568567 x = -1.1778568567 Simplifying x = -1.1778568567Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6064282853, -1.1778568567}
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