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Simplifying 9x2 + 58x + 73 = 0 Reorder the terms: 73 + 58x + 9x2 = 0 Solving 73 + 58x + 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'. 8.111111111 + 6.444444444x + x2 = 0 Move the constant term to the right: Add '-8.111111111' to each side of the equation. 8.111111111 + 6.444444444x + -8.111111111 + x2 = 0 + -8.111111111 Reorder the terms: 8.111111111 + -8.111111111 + 6.444444444x + x2 = 0 + -8.111111111 Combine like terms: 8.111111111 + -8.111111111 = 0.000000000 0.000000000 + 6.444444444x + x2 = 0 + -8.111111111 6.444444444x + x2 = 0 + -8.111111111 Combine like terms: 0 + -8.111111111 = -8.111111111 6.444444444x + x2 = -8.111111111 The x term is 6.444444444x. Take half its coefficient (3.222222222). Square it (10.38271605) and add it to both sides. Add '10.38271605' to each side of the equation. 6.444444444x + 10.38271605 + x2 = -8.111111111 + 10.38271605 Reorder the terms: 10.38271605 + 6.444444444x + x2 = -8.111111111 + 10.38271605 Combine like terms: -8.111111111 + 10.38271605 = 2.271604939 10.38271605 + 6.444444444x + x2 = 2.271604939 Factor a perfect square on the left side: (x + 3.222222222)(x + 3.222222222) = 2.271604939 Calculate the square root of the right side: 1.507184441 Break this problem into two subproblems by setting (x + 3.222222222) equal to 1.507184441 and -1.507184441.Subproblem 1
x + 3.222222222 = 1.507184441 Simplifying x + 3.222222222 = 1.507184441 Reorder the terms: 3.222222222 + x = 1.507184441 Solving 3.222222222 + x = 1.507184441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.222222222' to each side of the equation. 3.222222222 + -3.222222222 + x = 1.507184441 + -3.222222222 Combine like terms: 3.222222222 + -3.222222222 = 0.000000000 0.000000000 + x = 1.507184441 + -3.222222222 x = 1.507184441 + -3.222222222 Combine like terms: 1.507184441 + -3.222222222 = -1.715037781 x = -1.715037781 Simplifying x = -1.715037781Subproblem 2
x + 3.222222222 = -1.507184441 Simplifying x + 3.222222222 = -1.507184441 Reorder the terms: 3.222222222 + x = -1.507184441 Solving 3.222222222 + x = -1.507184441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.222222222' to each side of the equation. 3.222222222 + -3.222222222 + x = -1.507184441 + -3.222222222 Combine like terms: 3.222222222 + -3.222222222 = 0.000000000 0.000000000 + x = -1.507184441 + -3.222222222 x = -1.507184441 + -3.222222222 Combine like terms: -1.507184441 + -3.222222222 = -4.729406663 x = -4.729406663 Simplifying x = -4.729406663Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.715037781, -4.729406663}
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