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Simplifying x2 + -7x + -8 = 8 Reorder the terms: -8 + -7x + x2 = 8 Solving -8 + -7x + x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -8 + -7x + x2 = 8 + -8 Combine like terms: -8 + -8 = -16 -16 + -7x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -16 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -7x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -7x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -7x + x2 = 0 + 16 -7x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -7x + x2 = 16 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 16 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 16 + 12.25 Combine like terms: 16 + 12.25 = 28.25 12.25 + -7x + x2 = 28.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x + -3.5) equal to 5.315072906 and -5.315072906.Subproblem 1
x + -3.5 = 5.315072906 Simplifying x + -3.5 = 5.315072906 Reorder the terms: -3.5 + x = 5.315072906 Solving -3.5 + x = 5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 5.315072906 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 5.315072906 + 3.5 x = 5.315072906 + 3.5 Combine like terms: 5.315072906 + 3.5 = 8.815072906 x = 8.815072906 Simplifying x = 8.815072906Subproblem 2
x + -3.5 = -5.315072906 Simplifying x + -3.5 = -5.315072906 Reorder the terms: -3.5 + x = -5.315072906 Solving -3.5 + x = -5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -5.315072906 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -5.315072906 + 3.5 x = -5.315072906 + 3.5 Combine like terms: -5.315072906 + 3.5 = -1.815072906 x = -1.815072906 Simplifying x = -1.815072906Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.815072906, -1.815072906}
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