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Simplifying x2 + -8x + -81 = 0 Reorder the terms: -81 + -8x + x2 = 0 Solving -81 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + -8x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + -8x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -8x + x2 = 0 + 81 -8x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 -8x + x2 = 81 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 = 81 + 16 Reorder the terms: 16 + -8x + x2 = 81 + 16 Combine like terms: 81 + 16 = 97 16 + -8x + x2 = 97 Factor a perfect square on the left side: (x + -4)(x + -4) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (x + -4) equal to 9.848857802 and -9.848857802.Subproblem 1
x + -4 = 9.848857802 Simplifying x + -4 = 9.848857802 Reorder the terms: -4 + x = 9.848857802 Solving -4 + x = 9.848857802 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 = 9.848857802 + 4 Combine like terms: -4 + 4 = 0 0 + x = 9.848857802 + 4 x = 9.848857802 + 4 Combine like terms: 9.848857802 + 4 = 13.848857802 x = 13.848857802 Simplifying x = 13.848857802Subproblem 2
x + -4 = -9.848857802 Simplifying x + -4 = -9.848857802 Reorder the terms: -4 + x = -9.848857802 Solving -4 + x = -9.848857802 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 = -9.848857802 + 4 Combine like terms: -4 + 4 = 0 0 + x = -9.848857802 + 4 x = -9.848857802 + 4 Combine like terms: -9.848857802 + 4 = -5.848857802 x = -5.848857802 Simplifying x = -5.848857802Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.848857802, -5.848857802}
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