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Simplifying x2 + 150x + -3600 = 0 Reorder the terms: -3600 + 150x + x2 = 0 Solving -3600 + 150x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3600' to each side of the equation. -3600 + 150x + 3600 + x2 = 0 + 3600 Reorder the terms: -3600 + 3600 + 150x + x2 = 0 + 3600 Combine like terms: -3600 + 3600 = 0 0 + 150x + x2 = 0 + 3600 150x + x2 = 0 + 3600 Combine like terms: 0 + 3600 = 3600 150x + x2 = 3600 The x term is 150x. Take half its coefficient (75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. 150x + 5625 + x2 = 3600 + 5625 Reorder the terms: 5625 + 150x + x2 = 3600 + 5625 Combine like terms: 3600 + 5625 = 9225 5625 + 150x + x2 = 9225 Factor a perfect square on the left side: (x + 75)(x + 75) = 9225 Calculate the square root of the right side: 96.046863561 Break this problem into two subproblems by setting (x + 75) equal to 96.046863561 and -96.046863561.Subproblem 1
x + 75 = 96.046863561 Simplifying x + 75 = 96.046863561 Reorder the terms: 75 + x = 96.046863561 Solving 75 + x = 96.046863561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = 96.046863561 + -75 Combine like terms: 75 + -75 = 0 0 + x = 96.046863561 + -75 x = 96.046863561 + -75 Combine like terms: 96.046863561 + -75 = 21.046863561 x = 21.046863561 Simplifying x = 21.046863561Subproblem 2
x + 75 = -96.046863561 Simplifying x + 75 = -96.046863561 Reorder the terms: 75 + x = -96.046863561 Solving 75 + x = -96.046863561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = -96.046863561 + -75 Combine like terms: 75 + -75 = 0 0 + x = -96.046863561 + -75 x = -96.046863561 + -75 Combine like terms: -96.046863561 + -75 = -171.046863561 x = -171.046863561 Simplifying x = -171.046863561Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.046863561, -171.046863561}
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