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Simplifying x2 + 8x + -968 = 0 Reorder the terms: -968 + 8x + x2 = 0 Solving -968 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '968' to each side of the equation. -968 + 8x + 968 + x2 = 0 + 968 Reorder the terms: -968 + 968 + 8x + x2 = 0 + 968 Combine like terms: -968 + 968 = 0 0 + 8x + x2 = 0 + 968 8x + x2 = 0 + 968 Combine like terms: 0 + 968 = 968 8x + x2 = 968 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 = 968 + 16 Reorder the terms: 16 + 8x + x2 = 968 + 16 Combine like terms: 968 + 16 = 984 16 + 8x + x2 = 984 Factor a perfect square on the left side: (x + 4)(x + 4) = 984 Calculate the square root of the right side: 31.368774283 Break this problem into two subproblems by setting (x + 4) equal to 31.368774283 and -31.368774283.Subproblem 1
x + 4 = 31.368774283 Simplifying x + 4 = 31.368774283 Reorder the terms: 4 + x = 31.368774283 Solving 4 + x = 31.368774283 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 = 31.368774283 + -4 Combine like terms: 4 + -4 = 0 0 + x = 31.368774283 + -4 x = 31.368774283 + -4 Combine like terms: 31.368774283 + -4 = 27.368774283 x = 27.368774283 Simplifying x = 27.368774283Subproblem 2
x + 4 = -31.368774283 Simplifying x + 4 = -31.368774283 Reorder the terms: 4 + x = -31.368774283 Solving 4 + x = -31.368774283 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 = -31.368774283 + -4 Combine like terms: 4 + -4 = 0 0 + x = -31.368774283 + -4 x = -31.368774283 + -4 Combine like terms: -31.368774283 + -4 = -35.368774283 x = -35.368774283 Simplifying x = -35.368774283Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.368774283, -35.368774283}
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