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Simplifying 16x2 + 139 = 96x Reorder the terms: 139 + 16x2 = 96x Solving 139 + 16x2 = 96x Solving for variable 'x'. Reorder the terms: 139 + -96x + 16x2 = 96x + -96x Combine like terms: 96x + -96x = 0 139 + -96x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 8.6875 + -6x + x2 = 0 Move the constant term to the right: Add '-8.6875' to each side of the equation. 8.6875 + -6x + -8.6875 + x2 = 0 + -8.6875 Reorder the terms: 8.6875 + -8.6875 + -6x + x2 = 0 + -8.6875 Combine like terms: 8.6875 + -8.6875 = 0.0000 0.0000 + -6x + x2 = 0 + -8.6875 -6x + x2 = 0 + -8.6875 Combine like terms: 0 + -8.6875 = -8.6875 -6x + x2 = -8.6875 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -8.6875 + 9 Reorder the terms: 9 + -6x + x2 = -8.6875 + 9 Combine like terms: -8.6875 + 9 = 0.3125 9 + -6x + x2 = 0.3125 Factor a perfect square on the left side: (x + -3)(x + -3) = 0.3125 Calculate the square root of the right side: 0.559016994 Break this problem into two subproblems by setting (x + -3) equal to 0.559016994 and -0.559016994.Subproblem 1
x + -3 = 0.559016994 Simplifying x + -3 = 0.559016994 Reorder the terms: -3 + x = 0.559016994 Solving -3 + x = 0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0.559016994 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0.559016994 + 3 x = 0.559016994 + 3 Combine like terms: 0.559016994 + 3 = 3.559016994 x = 3.559016994 Simplifying x = 3.559016994Subproblem 2
x + -3 = -0.559016994 Simplifying x + -3 = -0.559016994 Reorder the terms: -3 + x = -0.559016994 Solving -3 + x = -0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -0.559016994 + 3 Combine like terms: -3 + 3 = 0 0 + x = -0.559016994 + 3 x = -0.559016994 + 3 Combine like terms: -0.559016994 + 3 = 2.440983006 x = 2.440983006 Simplifying x = 2.440983006Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.559016994, 2.440983006}
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