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Simplifying 6x(x + -5) = 3x + 3 Reorder the terms: 6x(-5 + x) = 3x + 3 (-5 * 6x + x * 6x) = 3x + 3 (-30x + 6x2) = 3x + 3 Reorder the terms: -30x + 6x2 = 3 + 3x Solving -30x + 6x2 = 3 + 3x Solving for variable 'x'. Reorder the terms: -3 + -30x + -3x + 6x2 = 3 + 3x + -3 + -3x Combine like terms: -30x + -3x = -33x -3 + -33x + 6x2 = 3 + 3x + -3 + -3x Reorder the terms: -3 + -33x + 6x2 = 3 + -3 + 3x + -3x Combine like terms: 3 + -3 = 0 -3 + -33x + 6x2 = 0 + 3x + -3x -3 + -33x + 6x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -3 + -33x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -11x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -11x + 2x2)' equal to zero and attempt to solve: Simplifying -1 + -11x + 2x2 = 0 Solving -1 + -11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -5.5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -5.5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -5.5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -5.5x + x2 = 0 + 0.5 -5.5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -5.5x + x2 = 0.5 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = 0.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 0.5 + 7.5625 Combine like terms: 0.5 + 7.5625 = 8.0625 7.5625 + -5.5x + x2 = 8.0625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (x + -2.75) equal to 2.839454173 and -2.839454173.Subproblem 1
x + -2.75 = 2.839454173 Simplifying x + -2.75 = 2.839454173 Reorder the terms: -2.75 + x = 2.839454173 Solving -2.75 + x = 2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 2.839454173 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 2.839454173 + 2.75 x = 2.839454173 + 2.75 Combine like terms: 2.839454173 + 2.75 = 5.589454173 x = 5.589454173 Simplifying x = 5.589454173Subproblem 2
x + -2.75 = -2.839454173 Simplifying x + -2.75 = -2.839454173 Reorder the terms: -2.75 + x = -2.839454173 Solving -2.75 + x = -2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -2.839454173 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -2.839454173 + 2.75 x = -2.839454173 + 2.75 Combine like terms: -2.839454173 + 2.75 = -0.089454173 x = -0.089454173 Simplifying x = -0.089454173Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.589454173, -0.089454173}Solution
x = {5.589454173, -0.089454173}
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