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Simplifying x * x + 150x + -15 = 0 Multiply x * x x2 + 150x + -15 = 0 Reorder the terms: -15 + 150x + x2 = 0 Solving -15 + 150x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 150x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 150x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 150x + x2 = 0 + 15 150x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 150x + x2 = 15 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 = 15 + 5625 Reorder the terms: 5625 + 150x + x2 = 15 + 5625 Combine like terms: 15 + 5625 = 5640 5625 + 150x + x2 = 5640 Factor a perfect square on the left side: (x + 75)(x + 75) = 5640 Calculate the square root of the right side: 75.099933422 Break this problem into two subproblems by setting (x + 75) equal to 75.099933422 and -75.099933422.Subproblem 1
x + 75 = 75.099933422 Simplifying x + 75 = 75.099933422 Reorder the terms: 75 + x = 75.099933422 Solving 75 + x = 75.099933422 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 = 75.099933422 + -75 Combine like terms: 75 + -75 = 0 0 + x = 75.099933422 + -75 x = 75.099933422 + -75 Combine like terms: 75.099933422 + -75 = 0.099933422 x = 0.099933422 Simplifying x = 0.099933422Subproblem 2
x + 75 = -75.099933422 Simplifying x + 75 = -75.099933422 Reorder the terms: 75 + x = -75.099933422 Solving 75 + x = -75.099933422 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 = -75.099933422 + -75 Combine like terms: 75 + -75 = 0 0 + x = -75.099933422 + -75 x = -75.099933422 + -75 Combine like terms: -75.099933422 + -75 = -150.099933422 x = -150.099933422 Simplifying x = -150.099933422Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.099933422, -150.099933422}
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