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Simplifying x2 + -45x + 8 = 0 Reorder the terms: 8 + -45x + x2 = 0 Solving 8 + -45x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -45x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -45x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -45x + x2 = 0 + -8 -45x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -45x + x2 = -8 The x term is -45x. Take half its coefficient (-22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. -45x + 506.25 + x2 = -8 + 506.25 Reorder the terms: 506.25 + -45x + x2 = -8 + 506.25 Combine like terms: -8 + 506.25 = 498.25 506.25 + -45x + x2 = 498.25 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 498.25 Calculate the square root of the right side: 22.321514286 Break this problem into two subproblems by setting (x + -22.5) equal to 22.321514286 and -22.321514286.Subproblem 1
x + -22.5 = 22.321514286 Simplifying x + -22.5 = 22.321514286 Reorder the terms: -22.5 + x = 22.321514286 Solving -22.5 + x = 22.321514286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = 22.321514286 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 22.321514286 + 22.5 x = 22.321514286 + 22.5 Combine like terms: 22.321514286 + 22.5 = 44.821514286 x = 44.821514286 Simplifying x = 44.821514286Subproblem 2
x + -22.5 = -22.321514286 Simplifying x + -22.5 = -22.321514286 Reorder the terms: -22.5 + x = -22.321514286 Solving -22.5 + x = -22.321514286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = -22.321514286 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -22.321514286 + 22.5 x = -22.321514286 + 22.5 Combine like terms: -22.321514286 + 22.5 = 0.178485714 x = 0.178485714 Simplifying x = 0.178485714Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.821514286, 0.178485714}
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