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Simplifying x2 + 150x + -5000 = 0 Reorder the terms: -5000 + 150x + x2 = 0 Solving -5000 + 150x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5000' to each side of the equation. -5000 + 150x + 5000 + x2 = 0 + 5000 Reorder the terms: -5000 + 5000 + 150x + x2 = 0 + 5000 Combine like terms: -5000 + 5000 = 0 0 + 150x + x2 = 0 + 5000 150x + x2 = 0 + 5000 Combine like terms: 0 + 5000 = 5000 150x + x2 = 5000 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 = 5000 + 5625 Reorder the terms: 5625 + 150x + x2 = 5000 + 5625 Combine like terms: 5000 + 5625 = 10625 5625 + 150x + x2 = 10625 Factor a perfect square on the left side: (x + 75)(x + 75) = 10625 Calculate the square root of the right side: 103.07764064 Break this problem into two subproblems by setting (x + 75) equal to 103.07764064 and -103.07764064.Subproblem 1
x + 75 = 103.07764064 Simplifying x + 75 = 103.07764064 Reorder the terms: 75 + x = 103.07764064 Solving 75 + x = 103.07764064 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 = 103.07764064 + -75 Combine like terms: 75 + -75 = 0 0 + x = 103.07764064 + -75 x = 103.07764064 + -75 Combine like terms: 103.07764064 + -75 = 28.07764064 x = 28.07764064 Simplifying x = 28.07764064Subproblem 2
x + 75 = -103.07764064 Simplifying x + 75 = -103.07764064 Reorder the terms: 75 + x = -103.07764064 Solving 75 + x = -103.07764064 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 = -103.07764064 + -75 Combine like terms: 75 + -75 = 0 0 + x = -103.07764064 + -75 x = -103.07764064 + -75 Combine like terms: -103.07764064 + -75 = -178.07764064 x = -178.07764064 Simplifying x = -178.07764064Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.07764064, -178.07764064}
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