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Simplifying 0.000001x2 + 500.025x + 150 = 0 Reorder the terms: 150 + 500.025x + 0.000001x2 = 0 Solving 150 + 500.025x + 0.000001x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.000001 the coefficient of the squared term: Divide each side by '0.000001'. 150000000 + 500025000x + x2 = 0 Move the constant term to the right: Add '-150000000' to each side of the equation. 150000000 + 500025000x + -150000000 + x2 = 0 + -150000000 Reorder the terms: 150000000 + -150000000 + 500025000x + x2 = 0 + -150000000 Combine like terms: 150000000 + -150000000 = 0 0 + 500025000x + x2 = 0 + -150000000 500025000x + x2 = 0 + -150000000 Combine like terms: 0 + -150000000 = -150000000 500025000x + x2 = -150000000 The x term is 500025000x. Take half its coefficient (250012500). Square it (62506250160000000) and add it to both sides. Add '62506250160000000' to each side of the equation. 500025000x + 62506250160000000 + x2 = -150000000 + 62506250160000000 Reorder the terms: 62506250160000000 + 500025000x + x2 = -150000000 + 62506250160000000 Combine like terms: -150000000 + 62506250160000000 = 62506250010000000 62506250160000000 + 500025000x + x2 = 62506250010000000 Factor a perfect square on the left side: (x + 250012500)(x + 250012500) = 62506250010000000 Calculate the square root of the right side: 250012499.707514624 Break this problem into two subproblems by setting (x + 250012500) equal to 250012499.707514624 and -250012499.707514624.Subproblem 1
x + 250012500 = 250012499.707514624 Simplifying x + 250012500 = 250012499.707514624 Reorder the terms: 250012500 + x = 250012499.707514624 Solving 250012500 + x = 250012499.707514624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250012500' to each side of the equation. 250012500 + -250012500 + x = 250012499.707514624 + -250012500 Combine like terms: 250012500 + -250012500 = 0 0 + x = 250012499.707514624 + -250012500 x = 250012499.707514624 + -250012500 Combine like terms: 250012499.707514624 + -250012500 = -0.292485376 x = -0.292485376 Simplifying x = -0.292485376Subproblem 2
x + 250012500 = -250012499.707514624 Simplifying x + 250012500 = -250012499.707514624 Reorder the terms: 250012500 + x = -250012499.707514624 Solving 250012500 + x = -250012499.707514624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250012500' to each side of the equation. 250012500 + -250012500 + x = -250012499.707514624 + -250012500 Combine like terms: 250012500 + -250012500 = 0 0 + x = -250012499.707514624 + -250012500 x = -250012499.707514624 + -250012500 Combine like terms: -250012499.707514624 + -250012500 = -500024999.707514624 x = -500024999.707514624 Simplifying x = -500024999.707514624Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.292485376, -500024999.707514624}
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