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Simplifying 6(X + 1) * 4X = 5 Reorder the terms: 6(1 + X) * 4X = 5 Reorder the terms for easier multiplication: 6 * 4X(1 + X) = 5 Multiply 6 * 4 24X(1 + X) = 5 (1 * 24X + X * 24X) = 5 (24X + 24X2) = 5 Solving 24X + 24X2 = 5 Solving for variable 'X'. Reorder the terms: -5 + 24X + 24X2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 24X + 24X2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.2083333333 + X + X2 = 0 Move the constant term to the right: Add '0.2083333333' to each side of the equation. -0.2083333333 + X + 0.2083333333 + X2 = 0 + 0.2083333333 Reorder the terms: -0.2083333333 + 0.2083333333 + X + X2 = 0 + 0.2083333333 Combine like terms: -0.2083333333 + 0.2083333333 = 0.0000000000 0.0000000000 + X + X2 = 0 + 0.2083333333 X + X2 = 0 + 0.2083333333 Combine like terms: 0 + 0.2083333333 = 0.2083333333 X + X2 = 0.2083333333 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. + 0.25 + X2 = 0.2083333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + X2 = 0.2083333333 + 0.25 Combine like terms: 0.2083333333 + 0.25 = 0.4583333333 1.25 + X2 = 0.4583333333 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 0.4583333333 Calculate the square root of the right side: 0.6770032 Break this problem into two subproblems by setting (X + 0.5) equal to 0.6770032 and -0.6770032.Subproblem 1
X + 0.5 = 0.6770032 Simplifying X + 0.5 = 0.6770032 Reorder the terms: 0.5 + X = 0.6770032 Solving 0.5 + X = 0.6770032 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 = 0.6770032 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 0.6770032 + -0.5 X = 0.6770032 + -0.5 Combine like terms: 0.6770032 + -0.5 = 0.1770032 X = 0.1770032 Simplifying X = 0.1770032Subproblem 2
X + 0.5 = -0.6770032 Simplifying X + 0.5 = -0.6770032 Reorder the terms: 0.5 + X = -0.6770032 Solving 0.5 + X = -0.6770032 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 = -0.6770032 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -0.6770032 + -0.5 X = -0.6770032 + -0.5 Combine like terms: -0.6770032 + -0.5 = -1.1770032 X = -1.1770032 Simplifying X = -1.1770032Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.1770032, -1.1770032}
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