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Simplifying x2 + -93x + 90 = 0 Reorder the terms: 90 + -93x + x2 = 0 Solving 90 + -93x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-90' to each side of the equation. 90 + -93x + -90 + x2 = 0 + -90 Reorder the terms: 90 + -90 + -93x + x2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + -93x + x2 = 0 + -90 -93x + x2 = 0 + -90 Combine like terms: 0 + -90 = -90 -93x + x2 = -90 The x term is -93x. Take half its coefficient (-46.5). Square it (2162.25) and add it to both sides. Add '2162.25' to each side of the equation. -93x + 2162.25 + x2 = -90 + 2162.25 Reorder the terms: 2162.25 + -93x + x2 = -90 + 2162.25 Combine like terms: -90 + 2162.25 = 2072.25 2162.25 + -93x + x2 = 2072.25 Factor a perfect square on the left side: (x + -46.5)(x + -46.5) = 2072.25 Calculate the square root of the right side: 45.521972716 Break this problem into two subproblems by setting (x + -46.5) equal to 45.521972716 and -45.521972716.Subproblem 1
x + -46.5 = 45.521972716 Simplifying x + -46.5 = 45.521972716 Reorder the terms: -46.5 + x = 45.521972716 Solving -46.5 + x = 45.521972716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '46.5' to each side of the equation. -46.5 + 46.5 + x = 45.521972716 + 46.5 Combine like terms: -46.5 + 46.5 = 0.0 0.0 + x = 45.521972716 + 46.5 x = 45.521972716 + 46.5 Combine like terms: 45.521972716 + 46.5 = 92.021972716 x = 92.021972716 Simplifying x = 92.021972716Subproblem 2
x + -46.5 = -45.521972716 Simplifying x + -46.5 = -45.521972716 Reorder the terms: -46.5 + x = -45.521972716 Solving -46.5 + x = -45.521972716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '46.5' to each side of the equation. -46.5 + 46.5 + x = -45.521972716 + 46.5 Combine like terms: -46.5 + 46.5 = 0.0 0.0 + x = -45.521972716 + 46.5 x = -45.521972716 + 46.5 Combine like terms: -45.521972716 + 46.5 = 0.978027284 x = 0.978027284 Simplifying x = 0.978027284Solution
The solution to the problem is based on the solutions from the subproblems. x = {92.021972716, 0.978027284}
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