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Simplifying x2 + -8x + -83 = 0 Reorder the terms: -83 + -8x + x2 = 0 Solving -83 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '83' to each side of the equation. -83 + -8x + 83 + x2 = 0 + 83 Reorder the terms: -83 + 83 + -8x + x2 = 0 + 83 Combine like terms: -83 + 83 = 0 0 + -8x + x2 = 0 + 83 -8x + x2 = 0 + 83 Combine like terms: 0 + 83 = 83 -8x + x2 = 83 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 = 83 + 16 Reorder the terms: 16 + -8x + x2 = 83 + 16 Combine like terms: 83 + 16 = 99 16 + -8x + x2 = 99 Factor a perfect square on the left side: (x + -4)(x + -4) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (x + -4) equal to 9.949874371 and -9.949874371.Subproblem 1
x + -4 = 9.949874371 Simplifying x + -4 = 9.949874371 Reorder the terms: -4 + x = 9.949874371 Solving -4 + x = 9.949874371 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 = 9.949874371 + 4 Combine like terms: -4 + 4 = 0 0 + x = 9.949874371 + 4 x = 9.949874371 + 4 Combine like terms: 9.949874371 + 4 = 13.949874371 x = 13.949874371 Simplifying x = 13.949874371Subproblem 2
x + -4 = -9.949874371 Simplifying x + -4 = -9.949874371 Reorder the terms: -4 + x = -9.949874371 Solving -4 + x = -9.949874371 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 = -9.949874371 + 4 Combine like terms: -4 + 4 = 0 0 + x = -9.949874371 + 4 x = -9.949874371 + 4 Combine like terms: -9.949874371 + 4 = -5.949874371 x = -5.949874371 Simplifying x = -5.949874371Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.949874371, -5.949874371}
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