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Simplifying 0.5x2 + 36x + -168 = 390 Reorder the terms: -168 + 36x + 0.5x2 = 390 Solving -168 + 36x + 0.5x2 = 390 Solving for variable 'x'. Reorder the terms: -168 + -390 + 36x + 0.5x2 = 390 + -390 Combine like terms: -168 + -390 = -558 -558 + 36x + 0.5x2 = 390 + -390 Combine like terms: 390 + -390 = 0 -558 + 36x + 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'. -1116 + 72x + x2 = 0 Move the constant term to the right: Add '1116' to each side of the equation. -1116 + 72x + 1116 + x2 = 0 + 1116 Reorder the terms: -1116 + 1116 + 72x + x2 = 0 + 1116 Combine like terms: -1116 + 1116 = 0 0 + 72x + x2 = 0 + 1116 72x + x2 = 0 + 1116 Combine like terms: 0 + 1116 = 1116 72x + x2 = 1116 The x term is 72x. Take half its coefficient (36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. 72x + 1296 + x2 = 1116 + 1296 Reorder the terms: 1296 + 72x + x2 = 1116 + 1296 Combine like terms: 1116 + 1296 = 2412 1296 + 72x + x2 = 2412 Factor a perfect square on the left side: (x + 36)(x + 36) = 2412 Calculate the square root of the right side: 49.112116631 Break this problem into two subproblems by setting (x + 36) equal to 49.112116631 and -49.112116631.Subproblem 1
x + 36 = 49.112116631 Simplifying x + 36 = 49.112116631 Reorder the terms: 36 + x = 49.112116631 Solving 36 + x = 49.112116631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -36 + x = 49.112116631 + -36 Combine like terms: 36 + -36 = 0 0 + x = 49.112116631 + -36 x = 49.112116631 + -36 Combine like terms: 49.112116631 + -36 = 13.112116631 x = 13.112116631 Simplifying x = 13.112116631Subproblem 2
x + 36 = -49.112116631 Simplifying x + 36 = -49.112116631 Reorder the terms: 36 + x = -49.112116631 Solving 36 + x = -49.112116631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -36 + x = -49.112116631 + -36 Combine like terms: 36 + -36 = 0 0 + x = -49.112116631 + -36 x = -49.112116631 + -36 Combine like terms: -49.112116631 + -36 = -85.112116631 x = -85.112116631 Simplifying x = -85.112116631Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.112116631, -85.112116631}
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