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Simplifying (16x2 + -49x + -91) = 0 Reorder the terms: (-91 + -49x + 16x2) = 0 Remove parenthesis around (-91 + -49x + 16x2) -91 + -49x + 16x2 = 0 Solving -91 + -49x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -5.6875 + -3.0625x + x2 = 0 Move the constant term to the right: Add '5.6875' to each side of the equation. -5.6875 + -3.0625x + 5.6875 + x2 = 0 + 5.6875 Reorder the terms: -5.6875 + 5.6875 + -3.0625x + x2 = 0 + 5.6875 Combine like terms: -5.6875 + 5.6875 = 0.0000 0.0000 + -3.0625x + x2 = 0 + 5.6875 -3.0625x + x2 = 0 + 5.6875 Combine like terms: 0 + 5.6875 = 5.6875 -3.0625x + x2 = 5.6875 The x term is -3.0625x. Take half its coefficient (-1.53125). Square it (2.344726563) and add it to both sides. Add '2.344726563' to each side of the equation. -3.0625x + 2.344726563 + x2 = 5.6875 + 2.344726563 Reorder the terms: 2.344726563 + -3.0625x + x2 = 5.6875 + 2.344726563 Combine like terms: 5.6875 + 2.344726563 = 8.032226563 2.344726563 + -3.0625x + x2 = 8.032226563 Factor a perfect square on the left side: (x + -1.53125)(x + -1.53125) = 8.032226563 Calculate the square root of the right side: 2.834118304 Break this problem into two subproblems by setting (x + -1.53125) equal to 2.834118304 and -2.834118304.Subproblem 1
x + -1.53125 = 2.834118304 Simplifying x + -1.53125 = 2.834118304 Reorder the terms: -1.53125 + x = 2.834118304 Solving -1.53125 + x = 2.834118304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.53125' to each side of the equation. -1.53125 + 1.53125 + x = 2.834118304 + 1.53125 Combine like terms: -1.53125 + 1.53125 = 0.00000 0.00000 + x = 2.834118304 + 1.53125 x = 2.834118304 + 1.53125 Combine like terms: 2.834118304 + 1.53125 = 4.365368304 x = 4.365368304 Simplifying x = 4.365368304Subproblem 2
x + -1.53125 = -2.834118304 Simplifying x + -1.53125 = -2.834118304 Reorder the terms: -1.53125 + x = -2.834118304 Solving -1.53125 + x = -2.834118304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.53125' to each side of the equation. -1.53125 + 1.53125 + x = -2.834118304 + 1.53125 Combine like terms: -1.53125 + 1.53125 = 0.00000 0.00000 + x = -2.834118304 + 1.53125 x = -2.834118304 + 1.53125 Combine like terms: -2.834118304 + 1.53125 = -1.302868304 x = -1.302868304 Simplifying x = -1.302868304Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.365368304, -1.302868304}
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