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Simplifying 49x2 + -1x + -0.4 = 0 Reorder the terms: -0.4 + -1x + 49x2 = 0 Solving -0.4 + -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'. -0.008163265306 + -0.02040816327x + x2 = 0 Move the constant term to the right: Add '0.008163265306' to each side of the equation. -0.008163265306 + -0.02040816327x + 0.008163265306 + x2 = 0 + 0.008163265306 Reorder the terms: -0.008163265306 + 0.008163265306 + -0.02040816327x + x2 = 0 + 0.008163265306 Combine like terms: -0.008163265306 + 0.008163265306 = 0.000000000000 0.000000000000 + -0.02040816327x + x2 = 0 + 0.008163265306 -0.02040816327x + x2 = 0 + 0.008163265306 Combine like terms: 0 + 0.008163265306 = 0.008163265306 -0.02040816327x + x2 = 0.008163265306 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 = 0.008163265306 + 0.0001041232821 Reorder the terms: 0.0001041232821 + -0.02040816327x + x2 = 0.008163265306 + 0.0001041232821 Combine like terms: 0.008163265306 + 0.0001041232821 = 0.0082673885881 0.0001041232821 + -0.02040816327x + x2 = 0.0082673885881 Factor a perfect square on the left side: (x + -0.01020408164)(x + -0.01020408164) = 0.0082673885881 Calculate the square root of the right side: 0.090925181 Break this problem into two subproblems by setting (x + -0.01020408164) equal to 0.090925181 and -0.090925181.Subproblem 1
x + -0.01020408164 = 0.090925181 Simplifying x + -0.01020408164 = 0.090925181 Reorder the terms: -0.01020408164 + x = 0.090925181 Solving -0.01020408164 + x = 0.090925181 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 = 0.090925181 + 0.01020408164 Combine like terms: -0.01020408164 + 0.01020408164 = 0.00000000000 0.00000000000 + x = 0.090925181 + 0.01020408164 x = 0.090925181 + 0.01020408164 Combine like terms: 0.090925181 + 0.01020408164 = 0.10112926264 x = 0.10112926264 Simplifying x = 0.10112926264Subproblem 2
x + -0.01020408164 = -0.090925181 Simplifying x + -0.01020408164 = -0.090925181 Reorder the terms: -0.01020408164 + x = -0.090925181 Solving -0.01020408164 + x = -0.090925181 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 = -0.090925181 + 0.01020408164 Combine like terms: -0.01020408164 + 0.01020408164 = 0.00000000000 0.00000000000 + x = -0.090925181 + 0.01020408164 x = -0.090925181 + 0.01020408164 Combine like terms: -0.090925181 + 0.01020408164 = -0.08072109936 x = -0.08072109936 Simplifying x = -0.08072109936Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.10112926264, -0.08072109936}
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