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Simplifying x2 + -45x + 265 = 0 Reorder the terms: 265 + -45x + x2 = 0 Solving 265 + -45x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-265' to each side of the equation. 265 + -45x + -265 + x2 = 0 + -265 Reorder the terms: 265 + -265 + -45x + x2 = 0 + -265 Combine like terms: 265 + -265 = 0 0 + -45x + x2 = 0 + -265 -45x + x2 = 0 + -265 Combine like terms: 0 + -265 = -265 -45x + x2 = -265 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 = -265 + 506.25 Reorder the terms: 506.25 + -45x + x2 = -265 + 506.25 Combine like terms: -265 + 506.25 = 241.25 506.25 + -45x + x2 = 241.25 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 241.25 Calculate the square root of the right side: 15.532224567 Break this problem into two subproblems by setting (x + -22.5) equal to 15.532224567 and -15.532224567.Subproblem 1
x + -22.5 = 15.532224567 Simplifying x + -22.5 = 15.532224567 Reorder the terms: -22.5 + x = 15.532224567 Solving -22.5 + x = 15.532224567 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 = 15.532224567 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 15.532224567 + 22.5 x = 15.532224567 + 22.5 Combine like terms: 15.532224567 + 22.5 = 38.032224567 x = 38.032224567 Simplifying x = 38.032224567Subproblem 2
x + -22.5 = -15.532224567 Simplifying x + -22.5 = -15.532224567 Reorder the terms: -22.5 + x = -15.532224567 Solving -22.5 + x = -15.532224567 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 = -15.532224567 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -15.532224567 + 22.5 x = -15.532224567 + 22.5 Combine like terms: -15.532224567 + 22.5 = 6.967775433 x = 6.967775433 Simplifying x = 6.967775433Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.032224567, 6.967775433}
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