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Simplifying 9x2 + 30x = 17 Reorder the terms: 30x + 9x2 = 17 Solving 30x + 9x2 = 17 Solving for variable 'x'. Reorder the terms: -17 + 30x + 9x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 30x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.888888889 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '1.888888889' to each side of the equation. -1.888888889 + 3.333333333x + 1.888888889 + x2 = 0 + 1.888888889 Reorder the terms: -1.888888889 + 1.888888889 + 3.333333333x + x2 = 0 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + 3.333333333x + x2 = 0 + 1.888888889 3.333333333x + x2 = 0 + 1.888888889 Combine like terms: 0 + 1.888888889 = 1.888888889 3.333333333x + x2 = 1.888888889 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 = 1.888888889 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 1.888888889 + 2.777777779 Combine like terms: 1.888888889 + 2.777777779 = 4.666666668 2.777777779 + 3.333333333x + x2 = 4.666666668 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 4.666666668 Calculate the square root of the right side: 2.1602469 Break this problem into two subproblems by setting (x + 1.666666667) equal to 2.1602469 and -2.1602469.Subproblem 1
x + 1.666666667 = 2.1602469 Simplifying x + 1.666666667 = 2.1602469 Reorder the terms: 1.666666667 + x = 2.1602469 Solving 1.666666667 + x = 2.1602469 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 = 2.1602469 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 2.1602469 + -1.666666667 x = 2.1602469 + -1.666666667 Combine like terms: 2.1602469 + -1.666666667 = 0.493580233 x = 0.493580233 Simplifying x = 0.493580233Subproblem 2
x + 1.666666667 = -2.1602469 Simplifying x + 1.666666667 = -2.1602469 Reorder the terms: 1.666666667 + x = -2.1602469 Solving 1.666666667 + x = -2.1602469 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 = -2.1602469 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -2.1602469 + -1.666666667 x = -2.1602469 + -1.666666667 Combine like terms: -2.1602469 + -1.666666667 = -3.826913567 x = -3.826913567 Simplifying x = -3.826913567Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.493580233, -3.826913567}
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