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Simplifying 9x2 = 30x + 35 Reorder the terms: 9x2 = 35 + 30x Solving 9x2 = 35 + 30x Solving for variable 'x'. Reorder the terms: -35 + -30x + 9x2 = 35 + 30x + -35 + -30x Reorder the terms: -35 + -30x + 9x2 = 35 + -35 + 30x + -30x Combine like terms: 35 + -35 = 0 -35 + -30x + 9x2 = 0 + 30x + -30x -35 + -30x + 9x2 = 30x + -30x Combine like terms: 30x + -30x = 0 -35 + -30x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.888888889 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '3.888888889' to each side of the equation. -3.888888889 + -3.333333333x + 3.888888889 + x2 = 0 + 3.888888889 Reorder the terms: -3.888888889 + 3.888888889 + -3.333333333x + x2 = 0 + 3.888888889 Combine like terms: -3.888888889 + 3.888888889 = 0.000000000 0.000000000 + -3.333333333x + x2 = 0 + 3.888888889 -3.333333333x + x2 = 0 + 3.888888889 Combine like terms: 0 + 3.888888889 = 3.888888889 -3.333333333x + x2 = 3.888888889 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = 3.888888889 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = 3.888888889 + 2.777777779 Combine like terms: 3.888888889 + 2.777777779 = 6.666666668 2.777777779 + -3.333333333x + x2 = 6.666666668 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 6.666666668 Calculate the square root of the right side: 2.581988898 Break this problem into two subproblems by setting (x + -1.666666667) equal to 2.581988898 and -2.581988898.Subproblem 1
x + -1.666666667 = 2.581988898 Simplifying x + -1.666666667 = 2.581988898 Reorder the terms: -1.666666667 + x = 2.581988898 Solving -1.666666667 + x = 2.581988898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 2.581988898 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 2.581988898 + 1.666666667 x = 2.581988898 + 1.666666667 Combine like terms: 2.581988898 + 1.666666667 = 4.248655565 x = 4.248655565 Simplifying x = 4.248655565Subproblem 2
x + -1.666666667 = -2.581988898 Simplifying x + -1.666666667 = -2.581988898 Reorder the terms: -1.666666667 + x = -2.581988898 Solving -1.666666667 + x = -2.581988898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -2.581988898 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -2.581988898 + 1.666666667 x = -2.581988898 + 1.666666667 Combine like terms: -2.581988898 + 1.666666667 = -0.915322231 x = -0.915322231 Simplifying x = -0.915322231Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.248655565, -0.915322231}
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