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Simplifying 9x(x + 6) + -1(9x + 2) = 1 Reorder the terms: 9x(6 + x) + -1(9x + 2) = 1 (6 * 9x + x * 9x) + -1(9x + 2) = 1 (54x + 9x2) + -1(9x + 2) = 1 Reorder the terms: 54x + 9x2 + -1(2 + 9x) = 1 54x + 9x2 + (2 * -1 + 9x * -1) = 1 54x + 9x2 + (-2 + -9x) = 1 Reorder the terms: -2 + 54x + -9x + 9x2 = 1 Combine like terms: 54x + -9x = 45x -2 + 45x + 9x2 = 1 Solving -2 + 45x + 9x2 = 1 Solving for variable 'x'. Reorder the terms: -2 + -1 + 45x + 9x2 = 1 + -1 Combine like terms: -2 + -1 = -3 -3 + 45x + 9x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -3 + 45x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 15x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + 15x + 3x2)' equal to zero and attempt to solve: Simplifying -1 + 15x + 3x2 = 0 Solving -1 + 15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + 5x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 5x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 5x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 5x + x2 = 0 + 0.3333333333 5x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 5x + x2 = 0.3333333333 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 0.3333333333 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 0.3333333333 + 6.25 Combine like terms: 0.3333333333 + 6.25 = 6.5833333333 6.25 + 5x + x2 = 6.5833333333 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 6.5833333333 Calculate the square root of the right side: 2.56580072 Break this problem into two subproblems by setting (x + 2.5) equal to 2.56580072 and -2.56580072.Subproblem 1
x + 2.5 = 2.56580072 Simplifying x + 2.5 = 2.56580072 Reorder the terms: 2.5 + x = 2.56580072 Solving 2.5 + x = 2.56580072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.56580072 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.56580072 + -2.5 x = 2.56580072 + -2.5 Combine like terms: 2.56580072 + -2.5 = 0.06580072 x = 0.06580072 Simplifying x = 0.06580072Subproblem 2
x + 2.5 = -2.56580072 Simplifying x + 2.5 = -2.56580072 Reorder the terms: 2.5 + x = -2.56580072 Solving 2.5 + x = -2.56580072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.56580072 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.56580072 + -2.5 x = -2.56580072 + -2.5 Combine like terms: -2.56580072 + -2.5 = -5.06580072 x = -5.06580072 Simplifying x = -5.06580072Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.06580072, -5.06580072}Solution
x = {0.06580072, -5.06580072}
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