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Simplifying 96x = 16x2 + 142 Reorder the terms: 96x = 142 + 16x2 Solving 96x = 142 + 16x2 Solving for variable 'x'. Reorder the terms: -142 + 96x + -16x2 = 142 + 16x2 + -142 + -16x2 Reorder the terms: -142 + 96x + -16x2 = 142 + -142 + 16x2 + -16x2 Combine like terms: 142 + -142 = 0 -142 + 96x + -16x2 = 0 + 16x2 + -16x2 -142 + 96x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -142 + 96x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-71 + 48x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-71 + 48x + -8x2)' equal to zero and attempt to solve: Simplifying -71 + 48x + -8x2 = 0 Solving -71 + 48x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 8.875 + -6x + x2 = 0 Move the constant term to the right: Add '-8.875' to each side of the equation. 8.875 + -6x + -8.875 + x2 = 0 + -8.875 Reorder the terms: 8.875 + -8.875 + -6x + x2 = 0 + -8.875 Combine like terms: 8.875 + -8.875 = 0.000 0.000 + -6x + x2 = 0 + -8.875 -6x + x2 = 0 + -8.875 Combine like terms: 0 + -8.875 = -8.875 -6x + x2 = -8.875 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 = -8.875 + 9 Reorder the terms: 9 + -6x + x2 = -8.875 + 9 Combine like terms: -8.875 + 9 = 0.125 9 + -6x + x2 = 0.125 Factor a perfect square on the left side: (x + -3)(x + -3) = 0.125 Calculate the square root of the right side: 0.353553391 Break this problem into two subproblems by setting (x + -3) equal to 0.353553391 and -0.353553391.Subproblem 1
x + -3 = 0.353553391 Simplifying x + -3 = 0.353553391 Reorder the terms: -3 + x = 0.353553391 Solving -3 + x = 0.353553391 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 = 0.353553391 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0.353553391 + 3 x = 0.353553391 + 3 Combine like terms: 0.353553391 + 3 = 3.353553391 x = 3.353553391 Simplifying x = 3.353553391Subproblem 2
x + -3 = -0.353553391 Simplifying x + -3 = -0.353553391 Reorder the terms: -3 + x = -0.353553391 Solving -3 + x = -0.353553391 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 = -0.353553391 + 3 Combine like terms: -3 + 3 = 0 0 + x = -0.353553391 + 3 x = -0.353553391 + 3 Combine like terms: -0.353553391 + 3 = 2.646446609 x = 2.646446609 Simplifying x = 2.646446609Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.353553391, 2.646446609}Solution
x = {3.353553391, 2.646446609}
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