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Simplifying x2 + -8x + -69 = 0 Reorder the terms: -69 + -8x + x2 = 0 Solving -69 + -8x + x2 = 0 Solving for variable 'x'. 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 = 13.219544457 x = 13.219544457 Simplifying x = 13.219544457Subproblem 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 = -5.219544457 x = -5.219544457 Simplifying x = -5.219544457Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.219544457, -5.219544457}
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