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Simplifying 390 = (111 + X)(X) Reorder the terms for easier multiplication: 390 = X(111 + X) 390 = (111 * X + X * X) 390 = (111X + X2) Solving 390 = 111X + X2 Solving for variable 'X'. Reorder the terms: 390 + -111X + -1X2 = 111X + -111X + X2 + -1X2 Combine like terms: 111X + -111X = 0 390 + -111X + -1X2 = 0 + X2 + -1X2 390 + -111X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 390 + -111X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -390 + 111X + X2 = 0 Move the constant term to the right: Add '390' to each side of the equation. -390 + 111X + 390 + X2 = 0 + 390 Reorder the terms: -390 + 390 + 111X + X2 = 0 + 390 Combine like terms: -390 + 390 = 0 0 + 111X + X2 = 0 + 390 111X + X2 = 0 + 390 Combine like terms: 0 + 390 = 390 111X + X2 = 390 The X term is 111X. Take half its coefficient (55.5). Square it (3080.25) and add it to both sides. Add '3080.25' to each side of the equation. 111X + 3080.25 + X2 = 390 + 3080.25 Reorder the terms: 3080.25 + 111X + X2 = 390 + 3080.25 Combine like terms: 390 + 3080.25 = 3470.25 3080.25 + 111X + X2 = 3470.25 Factor a perfect square on the left side: (X + 55.5)(X + 55.5) = 3470.25 Calculate the square root of the right side: 58.908827861 Break this problem into two subproblems by setting (X + 55.5) equal to 58.908827861 and -58.908827861.Subproblem 1
X + 55.5 = 58.908827861 Simplifying X + 55.5 = 58.908827861 Reorder the terms: 55.5 + X = 58.908827861 Solving 55.5 + X = 58.908827861 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-55.5' to each side of the equation. 55.5 + -55.5 + X = 58.908827861 + -55.5 Combine like terms: 55.5 + -55.5 = 0.0 0.0 + X = 58.908827861 + -55.5 X = 58.908827861 + -55.5 Combine like terms: 58.908827861 + -55.5 = 3.408827861 X = 3.408827861 Simplifying X = 3.408827861Subproblem 2
X + 55.5 = -58.908827861 Simplifying X + 55.5 = -58.908827861 Reorder the terms: 55.5 + X = -58.908827861 Solving 55.5 + X = -58.908827861 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-55.5' to each side of the equation. 55.5 + -55.5 + X = -58.908827861 + -55.5 Combine like terms: 55.5 + -55.5 = 0.0 0.0 + X = -58.908827861 + -55.5 X = -58.908827861 + -55.5 Combine like terms: -58.908827861 + -55.5 = -114.408827861 X = -114.408827861 Simplifying X = -114.408827861Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.408827861, -114.408827861}
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