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Simplifying 6x2 = 3x + 5 Reorder the terms: 6x2 = 5 + 3x Solving 6x2 = 5 + 3x Solving for variable 'x'. Reorder the terms: -5 + -3x + 6x2 = 5 + 3x + -5 + -3x Reorder the terms: -5 + -3x + 6x2 = 5 + -5 + 3x + -3x Combine like terms: 5 + -5 = 0 -5 + -3x + 6x2 = 0 + 3x + -3x -5 + -3x + 6x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -5 + -3x + 6x2 = 0 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 = 1.196484724 x = 1.196484724 Simplifying x = 1.196484724Subproblem 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 = -0.696484724 x = -0.696484724 Simplifying x = -0.696484724Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.196484724, -0.696484724}
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