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Simplifying 0.25X2 + 6X = 31 Reorder the terms: 6X + 0.25X2 = 31 Solving 6X + 0.25X2 = 31 Solving for variable 'X'. Reorder the terms: -31 + 6X + 0.25X2 = 31 + -31 Combine like terms: 31 + -31 = 0 -31 + 6X + 0.25X2 = 0 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -124 + 24X + X2 = 0 Move the constant term to the right: Add '124' to each side of the equation. -124 + 24X + 124 + X2 = 0 + 124 Reorder the terms: -124 + 124 + 24X + X2 = 0 + 124 Combine like terms: -124 + 124 = 0 0 + 24X + X2 = 0 + 124 24X + X2 = 0 + 124 Combine like terms: 0 + 124 = 124 24X + X2 = 124 The X term is 24X. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24X + 144 + X2 = 124 + 144 Reorder the terms: 144 + 24X + X2 = 124 + 144 Combine like terms: 124 + 144 = 268 144 + 24X + X2 = 268 Factor a perfect square on the left side: (X + 12)(X + 12) = 268 Calculate the square root of the right side: 16.370705544 Break this problem into two subproblems by setting (X + 12) equal to 16.370705544 and -16.370705544.Subproblem 1
X + 12 = 16.370705544 Simplifying X + 12 = 16.370705544 Reorder the terms: 12 + X = 16.370705544 Solving 12 + X = 16.370705544 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + X = 16.370705544 + -12 Combine like terms: 12 + -12 = 0 0 + X = 16.370705544 + -12 X = 16.370705544 + -12 Combine like terms: 16.370705544 + -12 = 4.370705544 X = 4.370705544 Simplifying X = 4.370705544Subproblem 2
X + 12 = -16.370705544 Simplifying X + 12 = -16.370705544 Reorder the terms: 12 + X = -16.370705544 Solving 12 + X = -16.370705544 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + X = -16.370705544 + -12 Combine like terms: 12 + -12 = 0 0 + X = -16.370705544 + -12 X = -16.370705544 + -12 Combine like terms: -16.370705544 + -12 = -28.370705544 X = -28.370705544 Simplifying X = -28.370705544Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.370705544, -28.370705544}
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