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Simplifying 9x2 + -40x + -35 = 0 Reorder the terms: -35 + -40x + 9x2 = 0 Solving -35 + -40x + 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 + -4.444444444x + x2 = 0 Move the constant term to the right: Add '3.888888889' to each side of the equation. -3.888888889 + -4.444444444x + 3.888888889 + x2 = 0 + 3.888888889 Reorder the terms: -3.888888889 + 3.888888889 + -4.444444444x + x2 = 0 + 3.888888889 Combine like terms: -3.888888889 + 3.888888889 = 0.000000000 0.000000000 + -4.444444444x + x2 = 0 + 3.888888889 -4.444444444x + x2 = 0 + 3.888888889 Combine like terms: 0 + 3.888888889 = 3.888888889 -4.444444444x + x2 = 3.888888889 The x term is -4.444444444x. Take half its coefficient (-2.222222222). Square it (4.938271604) and add it to both sides. Add '4.938271604' to each side of the equation. -4.444444444x + 4.938271604 + x2 = 3.888888889 + 4.938271604 Reorder the terms: 4.938271604 + -4.444444444x + x2 = 3.888888889 + 4.938271604 Combine like terms: 3.888888889 + 4.938271604 = 8.827160493 4.938271604 + -4.444444444x + x2 = 8.827160493 Factor a perfect square on the left side: (x + -2.222222222)(x + -2.222222222) = 8.827160493 Calculate the square root of the right side: 2.971053768 Break this problem into two subproblems by setting (x + -2.222222222) equal to 2.971053768 and -2.971053768.Subproblem 1
x + -2.222222222 = 2.971053768 Simplifying x + -2.222222222 = 2.971053768 Reorder the terms: -2.222222222 + x = 2.971053768 Solving -2.222222222 + x = 2.971053768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.222222222' to each side of the equation. -2.222222222 + 2.222222222 + x = 2.971053768 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + x = 2.971053768 + 2.222222222 x = 2.971053768 + 2.222222222 Combine like terms: 2.971053768 + 2.222222222 = 5.19327599 x = 5.19327599 Simplifying x = 5.19327599Subproblem 2
x + -2.222222222 = -2.971053768 Simplifying x + -2.222222222 = -2.971053768 Reorder the terms: -2.222222222 + x = -2.971053768 Solving -2.222222222 + x = -2.971053768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.222222222' to each side of the equation. -2.222222222 + 2.222222222 + x = -2.971053768 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + x = -2.971053768 + 2.222222222 x = -2.971053768 + 2.222222222 Combine like terms: -2.971053768 + 2.222222222 = -0.748831546 x = -0.748831546 Simplifying x = -0.748831546Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.19327599, -0.748831546}
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