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Simplifying 2x2 + 11x + -72 = 0 Reorder the terms: -72 + 11x + 2x2 = 0 Solving -72 + 11x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -36 + 5.5x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 5.5x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 5.5x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 5.5x + x2 = 0 + 36 5.5x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 5.5x + x2 = 36 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 36 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 36 + 7.5625 Combine like terms: 36 + 7.5625 = 43.5625 7.5625 + 5.5x + x2 = 43.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 43.5625 Calculate the square root of the right side: 6.600189391 Break this problem into two subproblems by setting (x + 2.75) equal to 6.600189391 and -6.600189391.Subproblem 1
x + 2.75 = 6.600189391 Simplifying x + 2.75 = 6.600189391 Reorder the terms: 2.75 + x = 6.600189391 Solving 2.75 + x = 6.600189391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 6.600189391 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 6.600189391 + -2.75 x = 6.600189391 + -2.75 Combine like terms: 6.600189391 + -2.75 = 3.850189391 x = 3.850189391 Simplifying x = 3.850189391Subproblem 2
x + 2.75 = -6.600189391 Simplifying x + 2.75 = -6.600189391 Reorder the terms: 2.75 + x = -6.600189391 Solving 2.75 + x = -6.600189391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -6.600189391 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -6.600189391 + -2.75 x = -6.600189391 + -2.75 Combine like terms: -6.600189391 + -2.75 = -9.350189391 x = -9.350189391 Simplifying x = -9.350189391Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.850189391, -9.350189391}
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