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Simplifying 9x2 + -4x + -35 = 0 Reorder the terms: -35 + -4x + 9x2 = 0 Solving -35 + -4x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.888888889 + -0.4444444444x + x2 = 0 Move the constant term to the right: Add '3.888888889' to each side of the equation. -3.888888889 + -0.4444444444x + 3.888888889 + x2 = 0 + 3.888888889 Reorder the terms: -3.888888889 + 3.888888889 + -0.4444444444x + x2 = 0 + 3.888888889 Combine like terms: -3.888888889 + 3.888888889 = 0.000000000 0.000000000 + -0.4444444444x + x2 = 0 + 3.888888889 -0.4444444444x + x2 = 0 + 3.888888889 Combine like terms: 0 + 3.888888889 = 3.888888889 -0.4444444444x + x2 = 3.888888889 The x term is -0.4444444444x. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444x + 0.04938271604 + x2 = 3.888888889 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444x + x2 = 3.888888889 + 0.04938271604 Combine like terms: 3.888888889 + 0.04938271604 = 3.93827160504 0.04938271604 + -0.4444444444x + x2 = 3.93827160504 Factor a perfect square on the left side: (x + -0.2222222222)(x + -0.2222222222) = 3.93827160504 Calculate the square root of the right side: 1.9845079 Break this problem into two subproblems by setting (x + -0.2222222222) equal to 1.9845079 and -1.9845079.Subproblem 1
x + -0.2222222222 = 1.9845079 Simplifying x + -0.2222222222 = 1.9845079 Reorder the terms: -0.2222222222 + x = 1.9845079 Solving -0.2222222222 + x = 1.9845079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = 1.9845079 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 1.9845079 + 0.2222222222 x = 1.9845079 + 0.2222222222 Combine like terms: 1.9845079 + 0.2222222222 = 2.2067301222 x = 2.2067301222 Simplifying x = 2.2067301222Subproblem 2
x + -0.2222222222 = -1.9845079 Simplifying x + -0.2222222222 = -1.9845079 Reorder the terms: -0.2222222222 + x = -1.9845079 Solving -0.2222222222 + x = -1.9845079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = -1.9845079 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -1.9845079 + 0.2222222222 x = -1.9845079 + 0.2222222222 Combine like terms: -1.9845079 + 0.2222222222 = -1.7622856778 x = -1.7622856778 Simplifying x = -1.7622856778Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2067301222, -1.7622856778}
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