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Simplifying 16x = 92 + -8x2 Solving 16x = 92 + -8x2 Solving for variable 'x'. Reorder the terms: -92 + 16x + 8x2 = 92 + -8x2 + -92 + 8x2 Reorder the terms: -92 + 16x + 8x2 = 92 + -92 + -8x2 + 8x2 Combine like terms: 92 + -92 = 0 -92 + 16x + 8x2 = 0 + -8x2 + 8x2 -92 + 16x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 -92 + 16x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-23 + 4x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-23 + 4x + 2x2)' equal to zero and attempt to solve: Simplifying -23 + 4x + 2x2 = 0 Solving -23 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11.5 + 2x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + 2x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + 2x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + 2x + x2 = 0 + 11.5 2x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 2x + x2 = 11.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 11.5 + 1 Reorder the terms: 1 + 2x + x2 = 11.5 + 1 Combine like terms: 11.5 + 1 = 12.5 1 + 2x + x2 = 12.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (x + 1) equal to 3.535533906 and -3.535533906.Subproblem 1
x + 1 = 3.535533906 Simplifying x + 1 = 3.535533906 Reorder the terms: 1 + x = 3.535533906 Solving 1 + x = 3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.535533906 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.535533906 + -1 x = 3.535533906 + -1 Combine like terms: 3.535533906 + -1 = 2.535533906 x = 2.535533906 Simplifying x = 2.535533906Subproblem 2
x + 1 = -3.535533906 Simplifying x + 1 = -3.535533906 Reorder the terms: 1 + x = -3.535533906 Solving 1 + x = -3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.535533906 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.535533906 + -1 x = -3.535533906 + -1 Combine like terms: -3.535533906 + -1 = -4.535533906 x = -4.535533906 Simplifying x = -4.535533906Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.535533906, -4.535533906}Solution
x = {2.535533906, -4.535533906}
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