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Simplifying 2x2 + 72x = -81 Reorder the terms: 72x + 2x2 = -81 Solving 72x + 2x2 = -81 Solving for variable 'x'. Reorder the terms: 81 + 72x + 2x2 = -81 + 81 Combine like terms: -81 + 81 = 0 81 + 72x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 40.5 + 36x + x2 = 0 Move the constant term to the right: Add '-40.5' to each side of the equation. 40.5 + 36x + -40.5 + x2 = 0 + -40.5 Reorder the terms: 40.5 + -40.5 + 36x + x2 = 0 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + 36x + x2 = 0 + -40.5 36x + x2 = 0 + -40.5 Combine like terms: 0 + -40.5 = -40.5 36x + x2 = -40.5 The x term is 36x. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36x + 324 + x2 = -40.5 + 324 Reorder the terms: 324 + 36x + x2 = -40.5 + 324 Combine like terms: -40.5 + 324 = 283.5 324 + 36x + x2 = 283.5 Factor a perfect square on the left side: (x + 18)(x + 18) = 283.5 Calculate the square root of the right side: 16.83745824 Break this problem into two subproblems by setting (x + 18) equal to 16.83745824 and -16.83745824.Subproblem 1
x + 18 = 16.83745824 Simplifying x + 18 = 16.83745824 Reorder the terms: 18 + x = 16.83745824 Solving 18 + x = 16.83745824 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 16.83745824 + -18 Combine like terms: 18 + -18 = 0 0 + x = 16.83745824 + -18 x = 16.83745824 + -18 Combine like terms: 16.83745824 + -18 = -1.16254176 x = -1.16254176 Simplifying x = -1.16254176Subproblem 2
x + 18 = -16.83745824 Simplifying x + 18 = -16.83745824 Reorder the terms: 18 + x = -16.83745824 Solving 18 + x = -16.83745824 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -16.83745824 + -18 Combine like terms: 18 + -18 = 0 0 + x = -16.83745824 + -18 x = -16.83745824 + -18 Combine like terms: -16.83745824 + -18 = -34.83745824 x = -34.83745824 Simplifying x = -34.83745824Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.16254176, -34.83745824}
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