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Simplifying 9x2 + -72x + -128 = 0 Reorder the terms: -128 + -72x + 9x2 = 0 Solving -128 + -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'. -14.22222222 + -8x + x2 = 0 Move the constant term to the right: Add '14.22222222' to each side of the equation. -14.22222222 + -8x + 14.22222222 + x2 = 0 + 14.22222222 Reorder the terms: -14.22222222 + 14.22222222 + -8x + x2 = 0 + 14.22222222 Combine like terms: -14.22222222 + 14.22222222 = 0.00000000 0.00000000 + -8x + x2 = 0 + 14.22222222 -8x + x2 = 0 + 14.22222222 Combine like terms: 0 + 14.22222222 = 14.22222222 -8x + x2 = 14.22222222 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 = 14.22222222 + 16 Reorder the terms: 16 + -8x + x2 = 14.22222222 + 16 Combine like terms: 14.22222222 + 16 = 30.22222222 16 + -8x + x2 = 30.22222222 Factor a perfect square on the left side: (x + -4)(x + -4) = 30.22222222 Calculate the square root of the right side: 5.497474167 Break this problem into two subproblems by setting (x + -4) equal to 5.497474167 and -5.497474167.Subproblem 1
x + -4 = 5.497474167 Simplifying x + -4 = 5.497474167 Reorder the terms: -4 + x = 5.497474167 Solving -4 + x = 5.497474167 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 = 5.497474167 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.497474167 + 4 x = 5.497474167 + 4 Combine like terms: 5.497474167 + 4 = 9.497474167 x = 9.497474167 Simplifying x = 9.497474167Subproblem 2
x + -4 = -5.497474167 Simplifying x + -4 = -5.497474167 Reorder the terms: -4 + x = -5.497474167 Solving -4 + x = -5.497474167 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 = -5.497474167 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.497474167 + 4 x = -5.497474167 + 4 Combine like terms: -5.497474167 + 4 = -1.497474167 x = -1.497474167 Simplifying x = -1.497474167Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.497474167, -1.497474167}
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