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Simplifying 9x2 + 35x + 30 = 0 Reorder the terms: 30 + 35x + 9x2 = 0 Solving 30 + 35x + 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'. 3.333333333 + 3.888888889x + x2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + 3.888888889x + -3.333333333 + x2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + 3.888888889x + x2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + 3.888888889x + x2 = 0 + -3.333333333 3.888888889x + x2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 3.888888889x + x2 = -3.333333333 The x term is 3.888888889x. Take half its coefficient (1.944444445). Square it (3.780864200) and add it to both sides. Add '3.780864200' to each side of the equation. 3.888888889x + 3.780864200 + x2 = -3.333333333 + 3.780864200 Reorder the terms: 3.780864200 + 3.888888889x + x2 = -3.333333333 + 3.780864200 Combine like terms: -3.333333333 + 3.780864200 = 0.447530867 3.780864200 + 3.888888889x + x2 = 0.447530867 Factor a perfect square on the left side: (x + 1.944444445)(x + 1.944444445) = 0.447530867 Calculate the square root of the right side: 0.668977479 Break this problem into two subproblems by setting (x + 1.944444445) equal to 0.668977479 and -0.668977479.Subproblem 1
x + 1.944444445 = 0.668977479 Simplifying x + 1.944444445 = 0.668977479 Reorder the terms: 1.944444445 + x = 0.668977479 Solving 1.944444445 + x = 0.668977479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.944444445' to each side of the equation. 1.944444445 + -1.944444445 + x = 0.668977479 + -1.944444445 Combine like terms: 1.944444445 + -1.944444445 = 0.000000000 0.000000000 + x = 0.668977479 + -1.944444445 x = 0.668977479 + -1.944444445 Combine like terms: 0.668977479 + -1.944444445 = -1.275466966 x = -1.275466966 Simplifying x = -1.275466966Subproblem 2
x + 1.944444445 = -0.668977479 Simplifying x + 1.944444445 = -0.668977479 Reorder the terms: 1.944444445 + x = -0.668977479 Solving 1.944444445 + x = -0.668977479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.944444445' to each side of the equation. 1.944444445 + -1.944444445 + x = -0.668977479 + -1.944444445 Combine like terms: 1.944444445 + -1.944444445 = 0.000000000 0.000000000 + x = -0.668977479 + -1.944444445 x = -0.668977479 + -1.944444445 Combine like terms: -0.668977479 + -1.944444445 = -2.613421924 x = -2.613421924 Simplifying x = -2.613421924Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.275466966, -2.613421924}
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