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Simplifying (3 + X) * 0.5X = 140 Reorder the terms for easier multiplication: 0.5X(3 + X) = 140 (3 * 0.5X + X * 0.5X) = 140 (1.5X + 0.5X2) = 140 Solving 1.5X + 0.5X2 = 140 Solving for variable 'X'. Reorder the terms: -140 + 1.5X + 0.5X2 = 140 + -140 Combine like terms: 140 + -140 = 0 -140 + 1.5X + 0.5X2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -280 + 3X + X2 = 0 Move the constant term to the right: Add '280' to each side of the equation. -280 + 3X + 280 + X2 = 0 + 280 Reorder the terms: -280 + 280 + 3X + X2 = 0 + 280 Combine like terms: -280 + 280 = 0 0 + 3X + X2 = 0 + 280 3X + X2 = 0 + 280 Combine like terms: 0 + 280 = 280 3X + X2 = 280 The X term is 3X. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3X + 2.25 + X2 = 280 + 2.25 Reorder the terms: 2.25 + 3X + X2 = 280 + 2.25 Combine like terms: 280 + 2.25 = 282.25 2.25 + 3X + X2 = 282.25 Factor a perfect square on the left side: (X + 1.5)(X + 1.5) = 282.25 Calculate the square root of the right side: 16.800297616 Break this problem into two subproblems by setting (X + 1.5) equal to 16.800297616 and -16.800297616.Subproblem 1
X + 1.5 = 16.800297616 Simplifying X + 1.5 = 16.800297616 Reorder the terms: 1.5 + X = 16.800297616 Solving 1.5 + X = 16.800297616 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + X = 16.800297616 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = 16.800297616 + -1.5 X = 16.800297616 + -1.5 Combine like terms: 16.800297616 + -1.5 = 15.300297616 X = 15.300297616 Simplifying X = 15.300297616Subproblem 2
X + 1.5 = -16.800297616 Simplifying X + 1.5 = -16.800297616 Reorder the terms: 1.5 + X = -16.800297616 Solving 1.5 + X = -16.800297616 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + X = -16.800297616 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = -16.800297616 + -1.5 X = -16.800297616 + -1.5 Combine like terms: -16.800297616 + -1.5 = -18.300297616 X = -18.300297616 Simplifying X = -18.300297616Solution
The solution to the problem is based on the solutions from the subproblems. X = {15.300297616, -18.300297616}
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