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Simplifying 45x2 + -190x + 50 = 0 Reorder the terms: 50 + -190x + 45x2 = 0 Solving 50 + -190x + 45x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(10 + -38x + 9x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(10 + -38x + 9x2)' equal to zero and attempt to solve: Simplifying 10 + -38x + 9x2 = 0 Solving 10 + -38x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.111111111 + -4.222222222x + x2 = 0 Move the constant term to the right: Add '-1.111111111' to each side of the equation. 1.111111111 + -4.222222222x + -1.111111111 + x2 = 0 + -1.111111111 Reorder the terms: 1.111111111 + -1.111111111 + -4.222222222x + x2 = 0 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + -4.222222222x + x2 = 0 + -1.111111111 -4.222222222x + x2 = 0 + -1.111111111 Combine like terms: 0 + -1.111111111 = -1.111111111 -4.222222222x + x2 = -1.111111111 The x term is -4.222222222x. Take half its coefficient (-2.111111111). Square it (4.456790123) and add it to both sides. Add '4.456790123' to each side of the equation. -4.222222222x + 4.456790123 + x2 = -1.111111111 + 4.456790123 Reorder the terms: 4.456790123 + -4.222222222x + x2 = -1.111111111 + 4.456790123 Combine like terms: -1.111111111 + 4.456790123 = 3.345679012 4.456790123 + -4.222222222x + x2 = 3.345679012 Factor a perfect square on the left side: (x + -2.111111111)(x + -2.111111111) = 3.345679012 Calculate the square root of the right side: 1.829119737 Break this problem into two subproblems by setting (x + -2.111111111) equal to 1.829119737 and -1.829119737.Subproblem 1
x + -2.111111111 = 1.829119737 Simplifying x + -2.111111111 = 1.829119737 Reorder the terms: -2.111111111 + x = 1.829119737 Solving -2.111111111 + x = 1.829119737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.111111111' to each side of the equation. -2.111111111 + 2.111111111 + x = 1.829119737 + 2.111111111 Combine like terms: -2.111111111 + 2.111111111 = 0.000000000 0.000000000 + x = 1.829119737 + 2.111111111 x = 1.829119737 + 2.111111111 Combine like terms: 1.829119737 + 2.111111111 = 3.940230848 x = 3.940230848 Simplifying x = 3.940230848Subproblem 2
x + -2.111111111 = -1.829119737 Simplifying x + -2.111111111 = -1.829119737 Reorder the terms: -2.111111111 + x = -1.829119737 Solving -2.111111111 + x = -1.829119737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.111111111' to each side of the equation. -2.111111111 + 2.111111111 + x = -1.829119737 + 2.111111111 Combine like terms: -2.111111111 + 2.111111111 = 0.000000000 0.000000000 + x = -1.829119737 + 2.111111111 x = -1.829119737 + 2.111111111 Combine like terms: -1.829119737 + 2.111111111 = 0.281991374 x = 0.281991374 Simplifying x = 0.281991374Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.940230848, 0.281991374}Solution
x = {3.940230848, 0.281991374}
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