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Simplifying 6x(2x + -1) + 5 = 6x + 6 Reorder the terms: 6x(-1 + 2x) + 5 = 6x + 6 (-1 * 6x + 2x * 6x) + 5 = 6x + 6 (-6x + 12x2) + 5 = 6x + 6 Reorder the terms: 5 + -6x + 12x2 = 6x + 6 Reorder the terms: 5 + -6x + 12x2 = 6 + 6x Solving 5 + -6x + 12x2 = 6 + 6x Solving for variable 'x'. Reorder the terms: 5 + -6 + -6x + -6x + 12x2 = 6 + 6x + -6 + -6x Combine like terms: 5 + -6 = -1 -1 + -6x + -6x + 12x2 = 6 + 6x + -6 + -6x Combine like terms: -6x + -6x = -12x -1 + -12x + 12x2 = 6 + 6x + -6 + -6x Reorder the terms: -1 + -12x + 12x2 = 6 + -6 + 6x + -6x Combine like terms: 6 + -6 = 0 -1 + -12x + 12x2 = 0 + 6x + -6x -1 + -12x + 12x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -1 + -12x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.08333333333 + -1x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + -1x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + -1x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + -1x + x2 = 0 + 0.08333333333 -1x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 -1x + x2 = 0.08333333333 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.08333333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.08333333333 + 0.25 Combine like terms: 0.08333333333 + 0.25 = 0.33333333333 0.25 + -1x + x2 = 0.33333333333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.33333333333 Calculate the square root of the right side: 0.577350269 Break this problem into two subproblems by setting (x + -0.5) equal to 0.577350269 and -0.577350269.Subproblem 1
x + -0.5 = 0.577350269 Simplifying x + -0.5 = 0.577350269 Reorder the terms: -0.5 + x = 0.577350269 Solving -0.5 + x = 0.577350269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.577350269 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.577350269 + 0.5 x = 0.577350269 + 0.5 Combine like terms: 0.577350269 + 0.5 = 1.077350269 x = 1.077350269 Simplifying x = 1.077350269Subproblem 2
x + -0.5 = -0.577350269 Simplifying x + -0.5 = -0.577350269 Reorder the terms: -0.5 + x = -0.577350269 Solving -0.5 + x = -0.577350269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.577350269 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.577350269 + 0.5 x = -0.577350269 + 0.5 Combine like terms: -0.577350269 + 0.5 = -0.077350269 x = -0.077350269 Simplifying x = -0.077350269Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.077350269, -0.077350269}
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