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Simplifying 24x2 + 8x2 + 2 = 5 + -6x Reorder the terms: 2 + 24x2 + 8x2 = 5 + -6x Combine like terms: 24x2 + 8x2 = 32x2 2 + 32x2 = 5 + -6x Solving 2 + 32x2 = 5 + -6x Solving for variable 'x'. Reorder the terms: 2 + -5 + 6x + 32x2 = 5 + -6x + -5 + 6x Combine like terms: 2 + -5 = -3 -3 + 6x + 32x2 = 5 + -6x + -5 + 6x Reorder the terms: -3 + 6x + 32x2 = 5 + -5 + -6x + 6x Combine like terms: 5 + -5 = 0 -3 + 6x + 32x2 = 0 + -6x + 6x -3 + 6x + 32x2 = -6x + 6x Combine like terms: -6x + 6x = 0 -3 + 6x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.09375 + 0.1875x + x2 = 0 Move the constant term to the right: Add '0.09375' to each side of the equation. -0.09375 + 0.1875x + 0.09375 + x2 = 0 + 0.09375 Reorder the terms: -0.09375 + 0.09375 + 0.1875x + x2 = 0 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + 0.1875x + x2 = 0 + 0.09375 0.1875x + x2 = 0 + 0.09375 Combine like terms: 0 + 0.09375 = 0.09375 0.1875x + x2 = 0.09375 The x term is 0.1875x. Take half its coefficient (0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. 0.1875x + 0.0087890625 + x2 = 0.09375 + 0.0087890625 Reorder the terms: 0.0087890625 + 0.1875x + x2 = 0.09375 + 0.0087890625 Combine like terms: 0.09375 + 0.0087890625 = 0.1025390625 0.0087890625 + 0.1875x + x2 = 0.1025390625 Factor a perfect square on the left side: (x + 0.09375)(x + 0.09375) = 0.1025390625 Calculate the square root of the right side: 0.320217211 Break this problem into two subproblems by setting (x + 0.09375) equal to 0.320217211 and -0.320217211.Subproblem 1
x + 0.09375 = 0.320217211 Simplifying x + 0.09375 = 0.320217211 Reorder the terms: 0.09375 + x = 0.320217211 Solving 0.09375 + x = 0.320217211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09375' to each side of the equation. 0.09375 + -0.09375 + x = 0.320217211 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = 0.320217211 + -0.09375 x = 0.320217211 + -0.09375 Combine like terms: 0.320217211 + -0.09375 = 0.226467211 x = 0.226467211 Simplifying x = 0.226467211Subproblem 2
x + 0.09375 = -0.320217211 Simplifying x + 0.09375 = -0.320217211 Reorder the terms: 0.09375 + x = -0.320217211 Solving 0.09375 + x = -0.320217211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09375' to each side of the equation. 0.09375 + -0.09375 + x = -0.320217211 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = -0.320217211 + -0.09375 x = -0.320217211 + -0.09375 Combine like terms: -0.320217211 + -0.09375 = -0.413967211 x = -0.413967211 Simplifying x = -0.413967211Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.226467211, -0.413967211}
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