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Simplifying x(x + -8) = 1089 Reorder the terms: x(-8 + x) = 1089 (-8 * x + x * x) = 1089 (-8x + x^{2}) = 1089 Solving -8x + x^{2}= 1089 Solving for variable 'x'. Reorder the terms: -1089 + -8x + x^{2}= 1089 + -1089 Combine like terms: 1089 + -1089 = 0 -1089 + -8x + x^{2}= 0 Begin completing the square. Move the constant term to the right: Add '1089' to each side of the equation. -1089 + -8x + 1089 + x^{2}= 0 + 1089 Reorder the terms: -1089 + 1089 + -8x + x^{2}= 0 + 1089 Combine like terms: -1089 + 1089 = 0 0 + -8x + x^{2}= 0 + 1089 -8x + x^{2}= 0 + 1089 Combine like terms: 0 + 1089 = 1089 -8x + x^{2}= 1089 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 + x^{2}= 1089 + 16 Reorder the terms: 16 + -8x + x^{2}= 1089 + 16 Combine like terms: 1089 + 16 = 1105 16 + -8x + x^{2}= 1105 Factor a perfect square on the left side: (x + -4)(x + -4) = 1105 Calculate the square root of the right side: 33.241540277 Break this problem into two subproblems by setting (x + -4) equal to 33.241540277 and -33.241540277.## Subproblem 1

x + -4 = 33.241540277 Simplifying x + -4 = 33.241540277 Reorder the terms: -4 + x = 33.241540277 Solving -4 + x = 33.241540277 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 = 33.241540277 + 4 Combine like terms: -4 + 4 = 0 0 + x = 33.241540277 + 4 x = 33.241540277 + 4 Combine like terms: 33.241540277 + 4 = 37.241540277 x = 37.241540277 Simplifying x = 37.241540277## Subproblem 2

x + -4 = -33.241540277 Simplifying x + -4 = -33.241540277 Reorder the terms: -4 + x = -33.241540277 Solving -4 + x = -33.241540277 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 = -33.241540277 + 4 Combine like terms: -4 + 4 = 0 0 + x = -33.241540277 + 4 x = -33.241540277 + 4 Combine like terms: -33.241540277 + 4 = -29.241540277 x = -29.241540277 Simplifying x = -29.241540277## Solution

The solution to the problem is based on the solutions from the subproblems. x = {37.241540277, -29.241540277}

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