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Simplifying 6X2 + X = 3 Reorder the terms: X + 6X2 = 3 Solving X + 6X2 = 3 Solving for variable 'X'. Reorder the terms: -3 + X + 6X2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + X + 6X2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + 0.1666666667X + X2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.1666666667X + 0.5 + X2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.1666666667X + X2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.1666666667X + X2 = 0 + 0.5 0.1666666667X + X2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.1666666667X + X2 = 0.5 The X term is X. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1666666667X + 0.25 + X2 = 0.5 + 0.25 Reorder the terms: 0.25 + 0.1666666667X + X2 = 0.5 + 0.25 Combine like terms: 0.5 + 0.25 = 0.75 0.25 + 0.1666666667X + X2 = 0.75 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 0.75 Calculate the square root of the right side: 0.866025404 Break this problem into two subproblems by setting (X + 0.5) equal to 0.866025404 and -0.866025404.Subproblem 1
X + 0.5 = 0.866025404 Simplifying X + 0.5 = 0.866025404 Reorder the terms: 0.5 + X = 0.866025404 Solving 0.5 + X = 0.866025404 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = 0.866025404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 0.866025404 + -0.5 X = 0.866025404 + -0.5 Combine like terms: 0.866025404 + -0.5 = 0.366025404 X = 0.366025404 Simplifying X = 0.366025404Subproblem 2
X + 0.5 = -0.866025404 Simplifying X + 0.5 = -0.866025404 Reorder the terms: 0.5 + X = -0.866025404 Solving 0.5 + X = -0.866025404 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = -0.866025404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -0.866025404 + -0.5 X = -0.866025404 + -0.5 Combine like terms: -0.866025404 + -0.5 = -1.366025404 X = -1.366025404 Simplifying X = -1.366025404Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.366025404, -1.366025404}
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