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Simplifying 9x2 + -85x + 109 = 0 Reorder the terms: 109 + -85x + 9x2 = 0 Solving 109 + -85x + 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'. 12.11111111 + -9.444444444x + x2 = 0 Move the constant term to the right: Add '-12.11111111' to each side of the equation. 12.11111111 + -9.444444444x + -12.11111111 + x2 = 0 + -12.11111111 Reorder the terms: 12.11111111 + -12.11111111 + -9.444444444x + x2 = 0 + -12.11111111 Combine like terms: 12.11111111 + -12.11111111 = 0.00000000 0.00000000 + -9.444444444x + x2 = 0 + -12.11111111 -9.444444444x + x2 = 0 + -12.11111111 Combine like terms: 0 + -12.11111111 = -12.11111111 -9.444444444x + x2 = -12.11111111 The x term is -9.444444444x. Take half its coefficient (-4.722222222). Square it (22.29938271) and add it to both sides. Add '22.29938271' to each side of the equation. -9.444444444x + 22.29938271 + x2 = -12.11111111 + 22.29938271 Reorder the terms: 22.29938271 + -9.444444444x + x2 = -12.11111111 + 22.29938271 Combine like terms: -12.11111111 + 22.29938271 = 10.1882716 22.29938271 + -9.444444444x + x2 = 10.1882716 Factor a perfect square on the left side: (x + -4.722222222)(x + -4.722222222) = 10.1882716 Calculate the square root of the right side: 3.191907204 Break this problem into two subproblems by setting (x + -4.722222222) equal to 3.191907204 and -3.191907204.Subproblem 1
x + -4.722222222 = 3.191907204 Simplifying x + -4.722222222 = 3.191907204 Reorder the terms: -4.722222222 + x = 3.191907204 Solving -4.722222222 + x = 3.191907204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.722222222' to each side of the equation. -4.722222222 + 4.722222222 + x = 3.191907204 + 4.722222222 Combine like terms: -4.722222222 + 4.722222222 = 0.000000000 0.000000000 + x = 3.191907204 + 4.722222222 x = 3.191907204 + 4.722222222 Combine like terms: 3.191907204 + 4.722222222 = 7.914129426 x = 7.914129426 Simplifying x = 7.914129426Subproblem 2
x + -4.722222222 = -3.191907204 Simplifying x + -4.722222222 = -3.191907204 Reorder the terms: -4.722222222 + x = -3.191907204 Solving -4.722222222 + x = -3.191907204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.722222222' to each side of the equation. -4.722222222 + 4.722222222 + x = -3.191907204 + 4.722222222 Combine like terms: -4.722222222 + 4.722222222 = 0.000000000 0.000000000 + x = -3.191907204 + 4.722222222 x = -3.191907204 + 4.722222222 Combine like terms: -3.191907204 + 4.722222222 = 1.530315018 x = 1.530315018 Simplifying x = 1.530315018Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.914129426, 1.530315018}
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