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Simplifying -1x2 + 44x + -96 = 0 Reorder the terms: -96 + 44x + -1x2 = 0 Solving -96 + 44x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 96 + -44x + x2 = 0 Move the constant term to the right: Add '-96' to each side of the equation. 96 + -44x + -96 + x2 = 0 + -96 Reorder the terms: 96 + -96 + -44x + x2 = 0 + -96 Combine like terms: 96 + -96 = 0 0 + -44x + x2 = 0 + -96 -44x + x2 = 0 + -96 Combine like terms: 0 + -96 = -96 -44x + x2 = -96 The x term is -44x. Take half its coefficient (-22). Square it (484) and add it to both sides. Add '484' to each side of the equation. -44x + 484 + x2 = -96 + 484 Reorder the terms: 484 + -44x + x2 = -96 + 484 Combine like terms: -96 + 484 = 388 484 + -44x + x2 = 388 Factor a perfect square on the left side: (x + -22)(x + -22) = 388 Calculate the square root of the right side: 19.697715604 Break this problem into two subproblems by setting (x + -22) equal to 19.697715604 and -19.697715604.Subproblem 1
x + -22 = 19.697715604 Simplifying x + -22 = 19.697715604 Reorder the terms: -22 + x = 19.697715604 Solving -22 + x = 19.697715604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = 19.697715604 + 22 Combine like terms: -22 + 22 = 0 0 + x = 19.697715604 + 22 x = 19.697715604 + 22 Combine like terms: 19.697715604 + 22 = 41.697715604 x = 41.697715604 Simplifying x = 41.697715604Subproblem 2
x + -22 = -19.697715604 Simplifying x + -22 = -19.697715604 Reorder the terms: -22 + x = -19.697715604 Solving -22 + x = -19.697715604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = -19.697715604 + 22 Combine like terms: -22 + 22 = 0 0 + x = -19.697715604 + 22 x = -19.697715604 + 22 Combine like terms: -19.697715604 + 22 = 2.302284396 x = 2.302284396 Simplifying x = 2.302284396Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.697715604, 2.302284396}
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