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Simplifying x2 + -180x + 100 = 0 Reorder the terms: 100 + -180x + x2 = 0 Solving 100 + -180x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -180x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -180x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -180x + x2 = 0 + -100 -180x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -180x + x2 = -100 The x term is -180x. Take half its coefficient (-90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. -180x + 8100 + x2 = -100 + 8100 Reorder the terms: 8100 + -180x + x2 = -100 + 8100 Combine like terms: -100 + 8100 = 8000 8100 + -180x + x2 = 8000 Factor a perfect square on the left side: (x + -90)(x + -90) = 8000 Calculate the square root of the right side: 89.4427191 Break this problem into two subproblems by setting (x + -90) equal to 89.4427191 and -89.4427191.Subproblem 1
x + -90 = 89.4427191 Simplifying x + -90 = 89.4427191 Reorder the terms: -90 + x = 89.4427191 Solving -90 + x = 89.4427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = 89.4427191 + 90 Combine like terms: -90 + 90 = 0 0 + x = 89.4427191 + 90 x = 89.4427191 + 90 Combine like terms: 89.4427191 + 90 = 179.4427191 x = 179.4427191 Simplifying x = 179.4427191Subproblem 2
x + -90 = -89.4427191 Simplifying x + -90 = -89.4427191 Reorder the terms: -90 + x = -89.4427191 Solving -90 + x = -89.4427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = -89.4427191 + 90 Combine like terms: -90 + 90 = 0 0 + x = -89.4427191 + 90 x = -89.4427191 + 90 Combine like terms: -89.4427191 + 90 = 0.5572809 x = 0.5572809 Simplifying x = 0.5572809Solution
The solution to the problem is based on the solutions from the subproblems. x = {179.4427191, 0.5572809}
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