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Simplifying 3x(3x + -1) + -5(3x + 1) = 0 Reorder the terms: 3x(-1 + 3x) + -5(3x + 1) = 0 (-1 * 3x + 3x * 3x) + -5(3x + 1) = 0 (-3x + 9x2) + -5(3x + 1) = 0 Reorder the terms: -3x + 9x2 + -5(1 + 3x) = 0 -3x + 9x2 + (1 * -5 + 3x * -5) = 0 -3x + 9x2 + (-5 + -15x) = 0 Reorder the terms: -5 + -3x + -15x + 9x2 = 0 Combine like terms: -3x + -15x = -18x -5 + -18x + 9x2 = 0 Solving -5 + -18x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + -2x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -2x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -2x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + 0.5555555556 -2x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -2x + x2 = 0.5555555556 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.5555555556 + 1 Reorder the terms: 1 + -2x + x2 = 0.5555555556 + 1 Combine like terms: 0.5555555556 + 1 = 1.5555555556 1 + -2x + x2 = 1.5555555556 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.5555555556 Calculate the square root of the right side: 1.247219129 Break this problem into two subproblems by setting (x + -1) equal to 1.247219129 and -1.247219129.Subproblem 1
x + -1 = 1.247219129 Simplifying x + -1 = 1.247219129 Reorder the terms: -1 + x = 1.247219129 Solving -1 + x = 1.247219129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.247219129 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.247219129 + 1 x = 1.247219129 + 1 Combine like terms: 1.247219129 + 1 = 2.247219129 x = 2.247219129 Simplifying x = 2.247219129Subproblem 2
x + -1 = -1.247219129 Simplifying x + -1 = -1.247219129 Reorder the terms: -1 + x = -1.247219129 Solving -1 + x = -1.247219129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.247219129 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.247219129 + 1 x = -1.247219129 + 1 Combine like terms: -1.247219129 + 1 = -0.247219129 x = -0.247219129 Simplifying x = -0.247219129Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.247219129, -0.247219129}
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