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Simplifying x2 + 8x + -1088 = 0 Reorder the terms: -1088 + 8x + x2 = 0 Solving -1088 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1088' to each side of the equation. -1088 + 8x + 1088 + x2 = 0 + 1088 Reorder the terms: -1088 + 1088 + 8x + x2 = 0 + 1088 Combine like terms: -1088 + 1088 = 0 0 + 8x + x2 = 0 + 1088 8x + x2 = 0 + 1088 Combine like terms: 0 + 1088 = 1088 8x + x2 = 1088 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 = 1088 + 16 Reorder the terms: 16 + 8x + x2 = 1088 + 16 Combine like terms: 1088 + 16 = 1104 16 + 8x + x2 = 1104 Factor a perfect square on the left side: (x + 4)(x + 4) = 1104 Calculate the square root of the right side: 33.226495452 Break this problem into two subproblems by setting (x + 4) equal to 33.226495452 and -33.226495452.Subproblem 1
x + 4 = 33.226495452 Simplifying x + 4 = 33.226495452 Reorder the terms: 4 + x = 33.226495452 Solving 4 + x = 33.226495452 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 = 33.226495452 + -4 Combine like terms: 4 + -4 = 0 0 + x = 33.226495452 + -4 x = 33.226495452 + -4 Combine like terms: 33.226495452 + -4 = 29.226495452 x = 29.226495452 Simplifying x = 29.226495452Subproblem 2
x + 4 = -33.226495452 Simplifying x + 4 = -33.226495452 Reorder the terms: 4 + x = -33.226495452 Solving 4 + x = -33.226495452 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 = -33.226495452 + -4 Combine like terms: 4 + -4 = 0 0 + x = -33.226495452 + -4 x = -33.226495452 + -4 Combine like terms: -33.226495452 + -4 = -37.226495452 x = -37.226495452 Simplifying x = -37.226495452Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.226495452, -37.226495452}
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