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Simplifying x2 + 8x + 96 = 165 Reorder the terms: 96 + 8x + x2 = 165 Solving 96 + 8x + x2 = 165 Solving for variable 'x'. Reorder the terms: 96 + -165 + 8x + x2 = 165 + -165 Combine like terms: 96 + -165 = -69 -69 + 8x + x2 = 165 + -165 Combine like terms: 165 + -165 = 0 -69 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '69' to each side of the equation. -69 + 8x + 69 + x2 = 0 + 69 Reorder the terms: -69 + 69 + 8x + x2 = 0 + 69 Combine like terms: -69 + 69 = 0 0 + 8x + x2 = 0 + 69 8x + x2 = 0 + 69 Combine like terms: 0 + 69 = 69 8x + x2 = 69 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 69 + 16 Reorder the terms: 16 + 8x + x2 = 69 + 16 Combine like terms: 69 + 16 = 85 16 + 8x + x2 = 85 Factor a perfect square on the left side: (x + 4)(x + 4) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (x + 4) equal to 9.219544457 and -9.219544457.Subproblem 1
x + 4 = 9.219544457 Simplifying x + 4 = 9.219544457 Reorder the terms: 4 + x = 9.219544457 Solving 4 + x = 9.219544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 9.219544457 + -4 Combine like terms: 4 + -4 = 0 0 + x = 9.219544457 + -4 x = 9.219544457 + -4 Combine like terms: 9.219544457 + -4 = 5.219544457 x = 5.219544457 Simplifying x = 5.219544457Subproblem 2
x + 4 = -9.219544457 Simplifying x + 4 = -9.219544457 Reorder the terms: 4 + x = -9.219544457 Solving 4 + x = -9.219544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -9.219544457 + -4 Combine like terms: 4 + -4 = 0 0 + x = -9.219544457 + -4 x = -9.219544457 + -4 Combine like terms: -9.219544457 + -4 = -13.219544457 x = -13.219544457 Simplifying x = -13.219544457Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.219544457, -13.219544457}
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