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Simplifying x2 + -45x + -300 = 0 Reorder the terms: -300 + -45x + x2 = 0 Solving -300 + -45x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + -45x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + -45x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + -45x + x2 = 0 + 300 -45x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 -45x + x2 = 300 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 = 300 + 506.25 Reorder the terms: 506.25 + -45x + x2 = 300 + 506.25 Combine like terms: 300 + 506.25 = 806.25 506.25 + -45x + x2 = 806.25 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 806.25 Calculate the square root of the right side: 28.394541729 Break this problem into two subproblems by setting (x + -22.5) equal to 28.394541729 and -28.394541729.Subproblem 1
x + -22.5 = 28.394541729 Simplifying x + -22.5 = 28.394541729 Reorder the terms: -22.5 + x = 28.394541729 Solving -22.5 + x = 28.394541729 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 = 28.394541729 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 28.394541729 + 22.5 x = 28.394541729 + 22.5 Combine like terms: 28.394541729 + 22.5 = 50.894541729 x = 50.894541729 Simplifying x = 50.894541729Subproblem 2
x + -22.5 = -28.394541729 Simplifying x + -22.5 = -28.394541729 Reorder the terms: -22.5 + x = -28.394541729 Solving -22.5 + x = -28.394541729 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 = -28.394541729 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -28.394541729 + 22.5 x = -28.394541729 + 22.5 Combine like terms: -28.394541729 + 22.5 = -5.894541729 x = -5.894541729 Simplifying x = -5.894541729Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.894541729, -5.894541729}
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