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Simplifying 6x2 + 3x + -5 = 0 Reorder the terms: -5 + 3x + 6x2 = 0 Solving -5 + 3x + 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'. -0.8333333333 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + 0.5x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + 0.5x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + 0.5x + x2 = 0 + 0.8333333333 0.5x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 0.5x + x2 = 0.8333333333 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.8333333333 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.8333333333 + 0.0625 Combine like terms: 0.8333333333 + 0.0625 = 0.8958333333 0.0625 + 0.5x + x2 = 0.8958333333 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.8958333333 Calculate the square root of the right side: 0.946484724 Break this problem into two subproblems by setting (x + 0.25) equal to 0.946484724 and -0.946484724.Subproblem 1
x + 0.25 = 0.946484724 Simplifying x + 0.25 = 0.946484724 Reorder the terms: 0.25 + x = 0.946484724 Solving 0.25 + x = 0.946484724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.946484724 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.946484724 + -0.25 x = 0.946484724 + -0.25 Combine like terms: 0.946484724 + -0.25 = 0.696484724 x = 0.696484724 Simplifying x = 0.696484724Subproblem 2
x + 0.25 = -0.946484724 Simplifying x + 0.25 = -0.946484724 Reorder the terms: 0.25 + x = -0.946484724 Solving 0.25 + x = -0.946484724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.946484724 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.946484724 + -0.25 x = -0.946484724 + -0.25 Combine like terms: -0.946484724 + -0.25 = -1.196484724 x = -1.196484724 Simplifying x = -1.196484724Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.696484724, -1.196484724}
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