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Simplifying 49x2 + -1x + -3 = 0 Reorder the terms: -3 + -1x + 49x2 = 0 Solving -3 + -1x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.0612244898 + -0.02040816327x + x2 = 0 Move the constant term to the right: Add '0.0612244898' to each side of the equation. -0.0612244898 + -0.02040816327x + 0.0612244898 + x2 = 0 + 0.0612244898 Reorder the terms: -0.0612244898 + 0.0612244898 + -0.02040816327x + x2 = 0 + 0.0612244898 Combine like terms: -0.0612244898 + 0.0612244898 = 0.0000000000 0.0000000000 + -0.02040816327x + x2 = 0 + 0.0612244898 -0.02040816327x + x2 = 0 + 0.0612244898 Combine like terms: 0 + 0.0612244898 = 0.0612244898 -0.02040816327x + x2 = 0.0612244898 The x term is -0.02040816327x. Take half its coefficient (-0.01020408164). Square it (0.0001041232821) and add it to both sides. Add '0.0001041232821' to each side of the equation. -0.02040816327x + 0.0001041232821 + x2 = 0.0612244898 + 0.0001041232821 Reorder the terms: 0.0001041232821 + -0.02040816327x + x2 = 0.0612244898 + 0.0001041232821 Combine like terms: 0.0612244898 + 0.0001041232821 = 0.0613286130821 0.0001041232821 + -0.02040816327x + x2 = 0.0613286130821 Factor a perfect square on the left side: (x + -0.01020408164)(x + -0.01020408164) = 0.0613286130821 Calculate the square root of the right side: 0.247646145 Break this problem into two subproblems by setting (x + -0.01020408164) equal to 0.247646145 and -0.247646145.Subproblem 1
x + -0.01020408164 = 0.247646145 Simplifying x + -0.01020408164 = 0.247646145 Reorder the terms: -0.01020408164 + x = 0.247646145 Solving -0.01020408164 + x = 0.247646145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01020408164' to each side of the equation. -0.01020408164 + 0.01020408164 + x = 0.247646145 + 0.01020408164 Combine like terms: -0.01020408164 + 0.01020408164 = 0.00000000000 0.00000000000 + x = 0.247646145 + 0.01020408164 x = 0.247646145 + 0.01020408164 Combine like terms: 0.247646145 + 0.01020408164 = 0.25785022664 x = 0.25785022664 Simplifying x = 0.25785022664Subproblem 2
x + -0.01020408164 = -0.247646145 Simplifying x + -0.01020408164 = -0.247646145 Reorder the terms: -0.01020408164 + x = -0.247646145 Solving -0.01020408164 + x = -0.247646145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01020408164' to each side of the equation. -0.01020408164 + 0.01020408164 + x = -0.247646145 + 0.01020408164 Combine like terms: -0.01020408164 + 0.01020408164 = 0.00000000000 0.00000000000 + x = -0.247646145 + 0.01020408164 x = -0.247646145 + 0.01020408164 Combine like terms: -0.247646145 + 0.01020408164 = -0.23744206336 x = -0.23744206336 Simplifying x = -0.23744206336Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.25785022664, -0.23744206336}
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