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Simplifying (3x + 5)(3x + 5) = 17 Reorder the terms: (5 + 3x)(3x + 5) = 17 Reorder the terms: (5 + 3x)(5 + 3x) = 17 Multiply (5 + 3x) * (5 + 3x) (5(5 + 3x) + 3x * (5 + 3x)) = 17 ((5 * 5 + 3x * 5) + 3x * (5 + 3x)) = 17 ((25 + 15x) + 3x * (5 + 3x)) = 17 (25 + 15x + (5 * 3x + 3x * 3x)) = 17 (25 + 15x + (15x + 9x2)) = 17 Combine like terms: 15x + 15x = 30x (25 + 30x + 9x2) = 17 Solving 25 + 30x + 9x2 = 17 Solving for variable 'x'. Reorder the terms: 25 + -17 + 30x + 9x2 = 17 + -17 Combine like terms: 25 + -17 = 8 8 + 30x + 9x2 = 17 + -17 Combine like terms: 17 + -17 = 0 8 + 30x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.8888888889 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '-0.8888888889' to each side of the equation. 0.8888888889 + 3.333333333x + -0.8888888889 + x2 = 0 + -0.8888888889 Reorder the terms: 0.8888888889 + -0.8888888889 + 3.333333333x + x2 = 0 + -0.8888888889 Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000 0.0000000000 + 3.333333333x + x2 = 0 + -0.8888888889 3.333333333x + x2 = 0 + -0.8888888889 Combine like terms: 0 + -0.8888888889 = -0.8888888889 3.333333333x + x2 = -0.8888888889 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 = -0.8888888889 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = -0.8888888889 + 2.777777779 Combine like terms: -0.8888888889 + 2.777777779 = 1.8888888901 2.777777779 + 3.333333333x + x2 = 1.8888888901 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 1.8888888901 Calculate the square root of the right side: 1.374368542 Break this problem into two subproblems by setting (x + 1.666666667) equal to 1.374368542 and -1.374368542.Subproblem 1
x + 1.666666667 = 1.374368542 Simplifying x + 1.666666667 = 1.374368542 Reorder the terms: 1.666666667 + x = 1.374368542 Solving 1.666666667 + x = 1.374368542 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 = 1.374368542 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 1.374368542 + -1.666666667 x = 1.374368542 + -1.666666667 Combine like terms: 1.374368542 + -1.666666667 = -0.292298125 x = -0.292298125 Simplifying x = -0.292298125Subproblem 2
x + 1.666666667 = -1.374368542 Simplifying x + 1.666666667 = -1.374368542 Reorder the terms: 1.666666667 + x = -1.374368542 Solving 1.666666667 + x = -1.374368542 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 = -1.374368542 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -1.374368542 + -1.666666667 x = -1.374368542 + -1.666666667 Combine like terms: -1.374368542 + -1.666666667 = -3.041035209 x = -3.041035209 Simplifying x = -3.041035209Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.292298125, -3.041035209}
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