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Simplifying x2 + 16x + -85 = -8 Reorder the terms: -85 + 16x + x2 = -8 Solving -85 + 16x + x2 = -8 Solving for variable 'x'. Reorder the terms: -85 + 8 + 16x + x2 = -8 + 8 Combine like terms: -85 + 8 = -77 -77 + 16x + x2 = -8 + 8 Combine like terms: -8 + 8 = 0 -77 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + 16x + 77 + x2 = 0 + 77 Reorder the terms: -77 + 77 + 16x + x2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 16x + x2 = 0 + 77 16x + x2 = 0 + 77 Combine like terms: 0 + 77 = 77 16x + x2 = 77 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 77 + 64 Reorder the terms: 64 + 16x + x2 = 77 + 64 Combine like terms: 77 + 64 = 141 64 + 16x + x2 = 141 Factor a perfect square on the left side: (x + 8)(x + 8) = 141 Calculate the square root of the right side: 11.874342087 Break this problem into two subproblems by setting (x + 8) equal to 11.874342087 and -11.874342087.Subproblem 1
x + 8 = 11.874342087 Simplifying x + 8 = 11.874342087 Reorder the terms: 8 + x = 11.874342087 Solving 8 + x = 11.874342087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 11.874342087 + -8 Combine like terms: 8 + -8 = 0 0 + x = 11.874342087 + -8 x = 11.874342087 + -8 Combine like terms: 11.874342087 + -8 = 3.874342087 x = 3.874342087 Simplifying x = 3.874342087Subproblem 2
x + 8 = -11.874342087 Simplifying x + 8 = -11.874342087 Reorder the terms: 8 + x = -11.874342087 Solving 8 + x = -11.874342087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -11.874342087 + -8 Combine like terms: 8 + -8 = 0 0 + x = -11.874342087 + -8 x = -11.874342087 + -8 Combine like terms: -11.874342087 + -8 = -19.874342087 x = -19.874342087 Simplifying x = -19.874342087Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.874342087, -19.874342087}
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