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Simplifying x2 + -600x + 300 = 0 Reorder the terms: 300 + -600x + x2 = 0 Solving 300 + -600x + 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 + -600x + -300 + x2 = 0 + -300 Reorder the terms: 300 + -300 + -600x + x2 = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -600x + x2 = 0 + -300 -600x + x2 = 0 + -300 Combine like terms: 0 + -300 = -300 -600x + x2 = -300 The x term is -600x. Take half its coefficient (-300). Square it (90000) and add it to both sides. Add '90000' to each side of the equation. -600x + 90000 + x2 = -300 + 90000 Reorder the terms: 90000 + -600x + x2 = -300 + 90000 Combine like terms: -300 + 90000 = 89700 90000 + -600x + x2 = 89700 Factor a perfect square on the left side: (x + -300)(x + -300) = 89700 Calculate the square root of the right side: 299.499582637 Break this problem into two subproblems by setting (x + -300) equal to 299.499582637 and -299.499582637.Subproblem 1
x + -300 = 299.499582637 Simplifying x + -300 = 299.499582637 Reorder the terms: -300 + x = 299.499582637 Solving -300 + x = 299.499582637 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + x = 299.499582637 + 300 Combine like terms: -300 + 300 = 0 0 + x = 299.499582637 + 300 x = 299.499582637 + 300 Combine like terms: 299.499582637 + 300 = 599.499582637 x = 599.499582637 Simplifying x = 599.499582637Subproblem 2
x + -300 = -299.499582637 Simplifying x + -300 = -299.499582637 Reorder the terms: -300 + x = -299.499582637 Solving -300 + x = -299.499582637 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + x = -299.499582637 + 300 Combine like terms: -300 + 300 = 0 0 + x = -299.499582637 + 300 x = -299.499582637 + 300 Combine like terms: -299.499582637 + 300 = 0.500417363 x = 0.500417363 Simplifying x = 0.500417363Solution
The solution to the problem is based on the solutions from the subproblems. x = {599.499582637, 0.500417363}
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