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Simplifying 9x2 + -40x + 37 = 0 Reorder the terms: 37 + -40x + 9x2 = 0 Solving 37 + -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'. 4.111111111 + -4.444444444x + x2 = 0 Move the constant term to the right: Add '-4.111111111' to each side of the equation. 4.111111111 + -4.444444444x + -4.111111111 + x2 = 0 + -4.111111111 Reorder the terms: 4.111111111 + -4.111111111 + -4.444444444x + x2 = 0 + -4.111111111 Combine like terms: 4.111111111 + -4.111111111 = 0.000000000 0.000000000 + -4.444444444x + x2 = 0 + -4.111111111 -4.444444444x + x2 = 0 + -4.111111111 Combine like terms: 0 + -4.111111111 = -4.111111111 -4.444444444x + x2 = -4.111111111 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 = -4.111111111 + 4.938271604 Reorder the terms: 4.938271604 + -4.444444444x + x2 = -4.111111111 + 4.938271604 Combine like terms: -4.111111111 + 4.938271604 = 0.827160493 4.938271604 + -4.444444444x + x2 = 0.827160493 Factor a perfect square on the left side: (x + -2.222222222)(x + -2.222222222) = 0.827160493 Calculate the square root of the right side: 0.909483641 Break this problem into two subproblems by setting (x + -2.222222222) equal to 0.909483641 and -0.909483641.Subproblem 1
x + -2.222222222 = 0.909483641 Simplifying x + -2.222222222 = 0.909483641 Reorder the terms: -2.222222222 + x = 0.909483641 Solving -2.222222222 + x = 0.909483641 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 = 0.909483641 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + x = 0.909483641 + 2.222222222 x = 0.909483641 + 2.222222222 Combine like terms: 0.909483641 + 2.222222222 = 3.131705863 x = 3.131705863 Simplifying x = 3.131705863Subproblem 2
x + -2.222222222 = -0.909483641 Simplifying x + -2.222222222 = -0.909483641 Reorder the terms: -2.222222222 + x = -0.909483641 Solving -2.222222222 + x = -0.909483641 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 = -0.909483641 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + x = -0.909483641 + 2.222222222 x = -0.909483641 + 2.222222222 Combine like terms: -0.909483641 + 2.222222222 = 1.312738581 x = 1.312738581 Simplifying x = 1.312738581Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.131705863, 1.312738581}
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