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Simplifying x = -16x2 + 96x + 4 Reorder the terms: x = 4 + 96x + -16x2 Solving x = 4 + 96x + -16x2 Solving for variable 'x'. Reorder the terms: -4 + x + -96x + 16x2 = 4 + 96x + -16x2 + -4 + -96x + 16x2 Combine like terms: x + -96x = -95x -4 + -95x + 16x2 = 4 + 96x + -16x2 + -4 + -96x + 16x2 Reorder the terms: -4 + -95x + 16x2 = 4 + -4 + 96x + -96x + -16x2 + 16x2 Combine like terms: 4 + -4 = 0 -4 + -95x + 16x2 = 0 + 96x + -96x + -16x2 + 16x2 -4 + -95x + 16x2 = 96x + -96x + -16x2 + 16x2 Combine like terms: 96x + -96x = 0 -4 + -95x + 16x2 = 0 + -16x2 + 16x2 -4 + -95x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -4 + -95x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.25 + -5.9375x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -5.9375x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -5.9375x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -5.9375x + x2 = 0 + 0.25 -5.9375x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -5.9375x + x2 = 0.25 The x term is -5.9375x. Take half its coefficient (-2.96875). Square it (8.813476563) and add it to both sides. Add '8.813476563' to each side of the equation. -5.9375x + 8.813476563 + x2 = 0.25 + 8.813476563 Reorder the terms: 8.813476563 + -5.9375x + x2 = 0.25 + 8.813476563 Combine like terms: 0.25 + 8.813476563 = 9.063476563 8.813476563 + -5.9375x + x2 = 9.063476563 Factor a perfect square on the left side: (x + -2.96875)(x + -2.96875) = 9.063476563 Calculate the square root of the right side: 3.010560839 Break this problem into two subproblems by setting (x + -2.96875) equal to 3.010560839 and -3.010560839.Subproblem 1
x + -2.96875 = 3.010560839 Simplifying x + -2.96875 = 3.010560839 Reorder the terms: -2.96875 + x = 3.010560839 Solving -2.96875 + x = 3.010560839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.96875' to each side of the equation. -2.96875 + 2.96875 + x = 3.010560839 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + x = 3.010560839 + 2.96875 x = 3.010560839 + 2.96875 Combine like terms: 3.010560839 + 2.96875 = 5.979310839 x = 5.979310839 Simplifying x = 5.979310839Subproblem 2
x + -2.96875 = -3.010560839 Simplifying x + -2.96875 = -3.010560839 Reorder the terms: -2.96875 + x = -3.010560839 Solving -2.96875 + x = -3.010560839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.96875' to each side of the equation. -2.96875 + 2.96875 + x = -3.010560839 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + x = -3.010560839 + 2.96875 x = -3.010560839 + 2.96875 Combine like terms: -3.010560839 + 2.96875 = -0.041810839 x = -0.041810839 Simplifying x = -0.041810839Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.979310839, -0.041810839}
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