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Simplifying 9x2 + 29x = 14 Reorder the terms: 29x + 9x2 = 14 Solving 29x + 9x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + 29x + 9x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 29x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.555555556 + 3.222222222x + x2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + 3.222222222x + 1.555555556 + x2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + 3.222222222x + x2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + 3.222222222x + x2 = 0 + 1.555555556 3.222222222x + x2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 3.222222222x + x2 = 1.555555556 The x term is 3.222222222x. Take half its coefficient (1.611111111). Square it (2.595679012) and add it to both sides. Add '2.595679012' to each side of the equation. 3.222222222x + 2.595679012 + x2 = 1.555555556 + 2.595679012 Reorder the terms: 2.595679012 + 3.222222222x + x2 = 1.555555556 + 2.595679012 Combine like terms: 1.555555556 + 2.595679012 = 4.151234568 2.595679012 + 3.222222222x + x2 = 4.151234568 Factor a perfect square on the left side: (x + 1.611111111)(x + 1.611111111) = 4.151234568 Calculate the square root of the right side: 2.037457869 Break this problem into two subproblems by setting (x + 1.611111111) equal to 2.037457869 and -2.037457869.Subproblem 1
x + 1.611111111 = 2.037457869 Simplifying x + 1.611111111 = 2.037457869 Reorder the terms: 1.611111111 + x = 2.037457869 Solving 1.611111111 + x = 2.037457869 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.611111111' to each side of the equation. 1.611111111 + -1.611111111 + x = 2.037457869 + -1.611111111 Combine like terms: 1.611111111 + -1.611111111 = 0.000000000 0.000000000 + x = 2.037457869 + -1.611111111 x = 2.037457869 + -1.611111111 Combine like terms: 2.037457869 + -1.611111111 = 0.426346758 x = 0.426346758 Simplifying x = 0.426346758Subproblem 2
x + 1.611111111 = -2.037457869 Simplifying x + 1.611111111 = -2.037457869 Reorder the terms: 1.611111111 + x = -2.037457869 Solving 1.611111111 + x = -2.037457869 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.611111111' to each side of the equation. 1.611111111 + -1.611111111 + x = -2.037457869 + -1.611111111 Combine like terms: 1.611111111 + -1.611111111 = 0.000000000 0.000000000 + x = -2.037457869 + -1.611111111 x = -2.037457869 + -1.611111111 Combine like terms: -2.037457869 + -1.611111111 = -3.64856898 x = -3.64856898 Simplifying x = -3.64856898Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.426346758, -3.64856898}
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