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Simplifying 9x2 + 72x + 11 = 0 Reorder the terms: 11 + 72x + 9x2 = 0 Solving 11 + 72x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.222222222 + 8x + x2 = 0 Move the constant term to the right: Add '-1.222222222' to each side of the equation. 1.222222222 + 8x + -1.222222222 + x2 = 0 + -1.222222222 Reorder the terms: 1.222222222 + -1.222222222 + 8x + x2 = 0 + -1.222222222 Combine like terms: 1.222222222 + -1.222222222 = 0.000000000 0.000000000 + 8x + x2 = 0 + -1.222222222 8x + x2 = 0 + -1.222222222 Combine like terms: 0 + -1.222222222 = -1.222222222 8x + x2 = -1.222222222 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -1.222222222 + 16 Reorder the terms: 16 + 8x + x2 = -1.222222222 + 16 Combine like terms: -1.222222222 + 16 = 14.777777778 16 + 8x + x2 = 14.777777778 Factor a perfect square on the left side: (x + 4)(x + 4) = 14.777777778 Calculate the square root of the right side: 3.844187532 Break this problem into two subproblems by setting (x + 4) equal to 3.844187532 and -3.844187532.Subproblem 1
x + 4 = 3.844187532 Simplifying x + 4 = 3.844187532 Reorder the terms: 4 + x = 3.844187532 Solving 4 + x = 3.844187532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3.844187532 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.844187532 + -4 x = 3.844187532 + -4 Combine like terms: 3.844187532 + -4 = -0.155812468 x = -0.155812468 Simplifying x = -0.155812468Subproblem 2
x + 4 = -3.844187532 Simplifying x + 4 = -3.844187532 Reorder the terms: 4 + x = -3.844187532 Solving 4 + x = -3.844187532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3.844187532 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.844187532 + -4 x = -3.844187532 + -4 Combine like terms: -3.844187532 + -4 = -7.844187532 x = -7.844187532 Simplifying x = -7.844187532Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.155812468, -7.844187532}
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