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Simplifying 6x2 + -3x = 2 Reorder the terms: -3x + 6x2 = 2 Solving -3x + 6x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + -3x + 6x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -3x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.3333333333 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.5x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.5x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.5x + x2 = 0 + 0.3333333333 -0.5x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.5x + x2 = 0.3333333333 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 = 0.3333333333 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.3333333333 + 0.0625 Combine like terms: 0.3333333333 + 0.0625 = 0.3958333333 0.0625 + -0.5x + x2 = 0.3958333333 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.3958333333 Calculate the square root of the right side: 0.62915287 Break this problem into two subproblems by setting (x + -0.25) equal to 0.62915287 and -0.62915287.Subproblem 1
x + -0.25 = 0.62915287 Simplifying x + -0.25 = 0.62915287 Reorder the terms: -0.25 + x = 0.62915287 Solving -0.25 + x = 0.62915287 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 = 0.62915287 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.62915287 + 0.25 x = 0.62915287 + 0.25 Combine like terms: 0.62915287 + 0.25 = 0.87915287 x = 0.87915287 Simplifying x = 0.87915287Subproblem 2
x + -0.25 = -0.62915287 Simplifying x + -0.25 = -0.62915287 Reorder the terms: -0.25 + x = -0.62915287 Solving -0.25 + x = -0.62915287 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 = -0.62915287 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.62915287 + 0.25 x = -0.62915287 + 0.25 Combine like terms: -0.62915287 + 0.25 = -0.37915287 x = -0.37915287 Simplifying x = -0.37915287Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.87915287, -0.37915287}
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