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Simplifying 6x(2x + -1) + -7x = 5x + -1 Reorder the terms: 6x(-1 + 2x) + -7x = 5x + -1 (-1 * 6x + 2x * 6x) + -7x = 5x + -1 (-6x + 12x2) + -7x = 5x + -1 Reorder the terms: -6x + -7x + 12x2 = 5x + -1 Combine like terms: -6x + -7x = -13x -13x + 12x2 = 5x + -1 Reorder the terms: -13x + 12x2 = -1 + 5x Solving -13x + 12x2 = -1 + 5x Solving for variable 'x'. Reorder the terms: 1 + -13x + -5x + 12x2 = -1 + 5x + 1 + -5x Combine like terms: -13x + -5x = -18x 1 + -18x + 12x2 = -1 + 5x + 1 + -5x Reorder the terms: 1 + -18x + 12x2 = -1 + 1 + 5x + -5x Combine like terms: -1 + 1 = 0 1 + -18x + 12x2 = 0 + 5x + -5x 1 + -18x + 12x2 = 5x + -5x Combine like terms: 5x + -5x = 0 1 + -18x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.08333333333 + -1.5x + x2 = 0 Move the constant term to the right: Add '-0.08333333333' to each side of the equation. 0.08333333333 + -1.5x + -0.08333333333 + x2 = 0 + -0.08333333333 Reorder the terms: 0.08333333333 + -0.08333333333 + -1.5x + x2 = 0 + -0.08333333333 Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000 0.00000000000 + -1.5x + x2 = 0 + -0.08333333333 -1.5x + x2 = 0 + -0.08333333333 Combine like terms: 0 + -0.08333333333 = -0.08333333333 -1.5x + x2 = -0.08333333333 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -0.08333333333 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -0.08333333333 + 0.5625 Combine like terms: -0.08333333333 + 0.5625 = 0.47916666667 0.5625 + -1.5x + x2 = 0.47916666667 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.47916666667 Calculate the square root of the right side: 0.692218655 Break this problem into two subproblems by setting (x + -0.75) equal to 0.692218655 and -0.692218655.Subproblem 1
x + -0.75 = 0.692218655 Simplifying x + -0.75 = 0.692218655 Reorder the terms: -0.75 + x = 0.692218655 Solving -0.75 + x = 0.692218655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.692218655 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.692218655 + 0.75 x = 0.692218655 + 0.75 Combine like terms: 0.692218655 + 0.75 = 1.442218655 x = 1.442218655 Simplifying x = 1.442218655Subproblem 2
x + -0.75 = -0.692218655 Simplifying x + -0.75 = -0.692218655 Reorder the terms: -0.75 + x = -0.692218655 Solving -0.75 + x = -0.692218655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.692218655 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.692218655 + 0.75 x = -0.692218655 + 0.75 Combine like terms: -0.692218655 + 0.75 = 0.057781345 x = 0.057781345 Simplifying x = 0.057781345Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.442218655, 0.057781345}
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