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Simplifying (3x + -1)(3x + 5) = x Reorder the terms: (-1 + 3x)(3x + 5) = x Reorder the terms: (-1 + 3x)(5 + 3x) = x Multiply (-1 + 3x) * (5 + 3x) (-1(5 + 3x) + 3x * (5 + 3x)) = x ((5 * -1 + 3x * -1) + 3x * (5 + 3x)) = x ((-5 + -3x) + 3x * (5 + 3x)) = x (-5 + -3x + (5 * 3x + 3x * 3x)) = x (-5 + -3x + (15x + 9x2)) = x Combine like terms: -3x + 15x = 12x (-5 + 12x + 9x2) = x Solving -5 + 12x + 9x2 = x Solving for variable 'x'. Reorder the terms: -5 + 12x + -1x + 9x2 = x + -1x Combine like terms: 12x + -1x = 11x -5 + 11x + 9x2 = x + -1x Combine like terms: x + -1x = 0 -5 + 11x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + 1.222222222x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 1.222222222x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 1.222222222x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 1.222222222x + x2 = 0 + 0.5555555556 1.222222222x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 1.222222222x + x2 = 0.5555555556 The x term is 1.222222222x. Take half its coefficient (0.611111111). Square it (0.3734567900) and add it to both sides. Add '0.3734567900' to each side of the equation. 1.222222222x + 0.3734567900 + x2 = 0.5555555556 + 0.3734567900 Reorder the terms: 0.3734567900 + 1.222222222x + x2 = 0.5555555556 + 0.3734567900 Combine like terms: 0.5555555556 + 0.3734567900 = 0.9290123456 0.3734567900 + 1.222222222x + x2 = 0.9290123456 Factor a perfect square on the left side: (x + 0.611111111)(x + 0.611111111) = 0.9290123456 Calculate the square root of the right side: 0.963852865 Break this problem into two subproblems by setting (x + 0.611111111) equal to 0.963852865 and -0.963852865.Subproblem 1
x + 0.611111111 = 0.963852865 Simplifying x + 0.611111111 = 0.963852865 Reorder the terms: 0.611111111 + x = 0.963852865 Solving 0.611111111 + x = 0.963852865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + x = 0.963852865 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + x = 0.963852865 + -0.611111111 x = 0.963852865 + -0.611111111 Combine like terms: 0.963852865 + -0.611111111 = 0.352741754 x = 0.352741754 Simplifying x = 0.352741754Subproblem 2
x + 0.611111111 = -0.963852865 Simplifying x + 0.611111111 = -0.963852865 Reorder the terms: 0.611111111 + x = -0.963852865 Solving 0.611111111 + x = -0.963852865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + x = -0.963852865 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + x = -0.963852865 + -0.611111111 x = -0.963852865 + -0.611111111 Combine like terms: -0.963852865 + -0.611111111 = -1.574963976 x = -1.574963976 Simplifying x = -1.574963976Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.352741754, -1.574963976}
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