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Simplifying 9x2 + 47x + 52 = 0 Reorder the terms: 52 + 47x + 9x2 = 0 Solving 52 + 47x + 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'. 5.777777778 + 5.222222222x + x2 = 0 Move the constant term to the right: Add '-5.777777778' to each side of the equation. 5.777777778 + 5.222222222x + -5.777777778 + x2 = 0 + -5.777777778 Reorder the terms: 5.777777778 + -5.777777778 + 5.222222222x + x2 = 0 + -5.777777778 Combine like terms: 5.777777778 + -5.777777778 = 0.000000000 0.000000000 + 5.222222222x + x2 = 0 + -5.777777778 5.222222222x + x2 = 0 + -5.777777778 Combine like terms: 0 + -5.777777778 = -5.777777778 5.222222222x + x2 = -5.777777778 The x term is 5.222222222x. Take half its coefficient (2.611111111). Square it (6.817901234) and add it to both sides. Add '6.817901234' to each side of the equation. 5.222222222x + 6.817901234 + x2 = -5.777777778 + 6.817901234 Reorder the terms: 6.817901234 + 5.222222222x + x2 = -5.777777778 + 6.817901234 Combine like terms: -5.777777778 + 6.817901234 = 1.040123456 6.817901234 + 5.222222222x + x2 = 1.040123456 Factor a perfect square on the left side: (x + 2.611111111)(x + 2.611111111) = 1.040123456 Calculate the square root of the right side: 1.01986443 Break this problem into two subproblems by setting (x + 2.611111111) equal to 1.01986443 and -1.01986443.Subproblem 1
x + 2.611111111 = 1.01986443 Simplifying x + 2.611111111 = 1.01986443 Reorder the terms: 2.611111111 + x = 1.01986443 Solving 2.611111111 + x = 1.01986443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.611111111' to each side of the equation. 2.611111111 + -2.611111111 + x = 1.01986443 + -2.611111111 Combine like terms: 2.611111111 + -2.611111111 = 0.000000000 0.000000000 + x = 1.01986443 + -2.611111111 x = 1.01986443 + -2.611111111 Combine like terms: 1.01986443 + -2.611111111 = -1.591246681 x = -1.591246681 Simplifying x = -1.591246681Subproblem 2
x + 2.611111111 = -1.01986443 Simplifying x + 2.611111111 = -1.01986443 Reorder the terms: 2.611111111 + x = -1.01986443 Solving 2.611111111 + x = -1.01986443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.611111111' to each side of the equation. 2.611111111 + -2.611111111 + x = -1.01986443 + -2.611111111 Combine like terms: 2.611111111 + -2.611111111 = 0.000000000 0.000000000 + x = -1.01986443 + -2.611111111 x = -1.01986443 + -2.611111111 Combine like terms: -1.01986443 + -2.611111111 = -3.630975541 x = -3.630975541 Simplifying x = -3.630975541Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.591246681, -3.630975541}
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