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Simplifying 6x2 + 9x + -2 = 0 Reorder the terms: -2 + 9x + 6x2 = 0 Solving -2 + 9x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.3333333333 + 1.5x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.5x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.5x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.5x + x2 = 0 + 0.3333333333 1.5x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 1.5x + x2 = 0.3333333333 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 = 0.3333333333 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 0.3333333333 + 0.5625 Combine like terms: 0.3333333333 + 0.5625 = 0.8958333333 0.5625 + 1.5x + x2 = 0.8958333333 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 0.8958333333 Calculate the square root of the right side: 0.946484724 Break this problem into two subproblems by setting (x + 0.75) equal to 0.946484724 and -0.946484724.Subproblem 1
x + 0.75 = 0.946484724 Simplifying x + 0.75 = 0.946484724 Reorder the terms: 0.75 + x = 0.946484724 Solving 0.75 + x = 0.946484724 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 = 0.946484724 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 0.946484724 + -0.75 x = 0.946484724 + -0.75 Combine like terms: 0.946484724 + -0.75 = 0.196484724 x = 0.196484724 Simplifying x = 0.196484724Subproblem 2
x + 0.75 = -0.946484724 Simplifying x + 0.75 = -0.946484724 Reorder the terms: 0.75 + x = -0.946484724 Solving 0.75 + x = -0.946484724 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 = -0.946484724 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -0.946484724 + -0.75 x = -0.946484724 + -0.75 Combine like terms: -0.946484724 + -0.75 = -1.696484724 x = -1.696484724 Simplifying x = -1.696484724Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.196484724, -1.696484724}
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