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Simplifying x2 + -75x + 600 = 0 Reorder the terms: 600 + -75x + x2 = 0 Solving 600 + -75x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-600' to each side of the equation. 600 + -75x + -600 + x2 = 0 + -600 Reorder the terms: 600 + -600 + -75x + x2 = 0 + -600 Combine like terms: 600 + -600 = 0 0 + -75x + x2 = 0 + -600 -75x + x2 = 0 + -600 Combine like terms: 0 + -600 = -600 -75x + x2 = -600 The x term is -75x. Take half its coefficient (-37.5). Square it (1406.25) and add it to both sides. Add '1406.25' to each side of the equation. -75x + 1406.25 + x2 = -600 + 1406.25 Reorder the terms: 1406.25 + -75x + x2 = -600 + 1406.25 Combine like terms: -600 + 1406.25 = 806.25 1406.25 + -75x + x2 = 806.25 Factor a perfect square on the left side: (x + -37.5)(x + -37.5) = 806.25 Calculate the square root of the right side: 28.394541729 Break this problem into two subproblems by setting (x + -37.5) equal to 28.394541729 and -28.394541729.Subproblem 1
x + -37.5 = 28.394541729 Simplifying x + -37.5 = 28.394541729 Reorder the terms: -37.5 + x = 28.394541729 Solving -37.5 + x = 28.394541729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = 28.394541729 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = 28.394541729 + 37.5 x = 28.394541729 + 37.5 Combine like terms: 28.394541729 + 37.5 = 65.894541729 x = 65.894541729 Simplifying x = 65.894541729Subproblem 2
x + -37.5 = -28.394541729 Simplifying x + -37.5 = -28.394541729 Reorder the terms: -37.5 + x = -28.394541729 Solving -37.5 + x = -28.394541729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = -28.394541729 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = -28.394541729 + 37.5 x = -28.394541729 + 37.5 Combine like terms: -28.394541729 + 37.5 = 9.105458271 x = 9.105458271 Simplifying x = 9.105458271Solution
The solution to the problem is based on the solutions from the subproblems. x = {65.894541729, 9.105458271}
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