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Simplifying 0 = x2 + 600x + -5625 Reorder the terms: 0 = -5625 + 600x + x2 Solving 0 = -5625 + 600x + x2 Solving for variable 'x'. Combine like terms: 0 + 5625 = 5625 5625 + -600x + -1x2 = -5625 + 600x + x2 + 5625 + -600x + -1x2 Reorder the terms: 5625 + -600x + -1x2 = -5625 + 5625 + 600x + -600x + x2 + -1x2 Combine like terms: -5625 + 5625 = 0 5625 + -600x + -1x2 = 0 + 600x + -600x + x2 + -1x2 5625 + -600x + -1x2 = 600x + -600x + x2 + -1x2 Combine like terms: 600x + -600x = 0 5625 + -600x + -1x2 = 0 + x2 + -1x2 5625 + -600x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5625 + -600x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5625 + 600x + x2 = 0 Move the constant term to the right: Add '5625' to each side of the equation. -5625 + 600x + 5625 + x2 = 0 + 5625 Reorder the terms: -5625 + 5625 + 600x + x2 = 0 + 5625 Combine like terms: -5625 + 5625 = 0 0 + 600x + x2 = 0 + 5625 600x + x2 = 0 + 5625 Combine like terms: 0 + 5625 = 5625 600x + x2 = 5625 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 = 5625 + 90000 Reorder the terms: 90000 + 600x + x2 = 5625 + 90000 Combine like terms: 5625 + 90000 = 95625 90000 + 600x + x2 = 95625 Factor a perfect square on the left side: (x + 300)(x + 300) = 95625 Calculate the square root of the right side: 309.232921921 Break this problem into two subproblems by setting (x + 300) equal to 309.232921921 and -309.232921921.Subproblem 1
x + 300 = 309.232921921 Simplifying x + 300 = 309.232921921 Reorder the terms: 300 + x = 309.232921921 Solving 300 + x = 309.232921921 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 = 309.232921921 + -300 Combine like terms: 300 + -300 = 0 0 + x = 309.232921921 + -300 x = 309.232921921 + -300 Combine like terms: 309.232921921 + -300 = 9.232921921 x = 9.232921921 Simplifying x = 9.232921921Subproblem 2
x + 300 = -309.232921921 Simplifying x + 300 = -309.232921921 Reorder the terms: 300 + x = -309.232921921 Solving 300 + x = -309.232921921 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 = -309.232921921 + -300 Combine like terms: 300 + -300 = 0 0 + x = -309.232921921 + -300 x = -309.232921921 + -300 Combine like terms: -309.232921921 + -300 = -609.232921921 x = -609.232921921 Simplifying x = -609.232921921Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.232921921, -609.232921921}
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