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Simplifying 49x2 + -4 = x Reorder the terms: -4 + 49x2 = x Solving -4 + 49x2 = x Solving for variable 'x'. Reorder the terms: -4 + -1x + 49x2 = x + -1x Combine like terms: x + -1x = 0 -4 + -1x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.08163265306 + -0.02040816327x + x2 = 0 Move the constant term to the right: Add '0.08163265306' to each side of the equation. -0.08163265306 + -0.02040816327x + 0.08163265306 + x2 = 0 + 0.08163265306 Reorder the terms: -0.08163265306 + 0.08163265306 + -0.02040816327x + x2 = 0 + 0.08163265306 Combine like terms: -0.08163265306 + 0.08163265306 = 0.00000000000 0.00000000000 + -0.02040816327x + x2 = 0 + 0.08163265306 -0.02040816327x + x2 = 0 + 0.08163265306 Combine like terms: 0 + 0.08163265306 = 0.08163265306 -0.02040816327x + x2 = 0.08163265306 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 = 0.08163265306 + 0.0001041232821 Reorder the terms: 0.0001041232821 + -0.02040816327x + x2 = 0.08163265306 + 0.0001041232821 Combine like terms: 0.08163265306 + 0.0001041232821 = 0.0817367763421 0.0001041232821 + -0.02040816327x + x2 = 0.0817367763421 Factor a perfect square on the left side: (x + -0.01020408164)(x + -0.01020408164) = 0.0817367763421 Calculate the square root of the right side: 0.285896443 Break this problem into two subproblems by setting (x + -0.01020408164) equal to 0.285896443 and -0.285896443.Subproblem 1
x + -0.01020408164 = 0.285896443 Simplifying x + -0.01020408164 = 0.285896443 Reorder the terms: -0.01020408164 + x = 0.285896443 Solving -0.01020408164 + x = 0.285896443 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 = 0.285896443 + 0.01020408164 Combine like terms: -0.01020408164 + 0.01020408164 = 0.00000000000 0.00000000000 + x = 0.285896443 + 0.01020408164 x = 0.285896443 + 0.01020408164 Combine like terms: 0.285896443 + 0.01020408164 = 0.29610052464 x = 0.29610052464 Simplifying x = 0.29610052464Subproblem 2
x + -0.01020408164 = -0.285896443 Simplifying x + -0.01020408164 = -0.285896443 Reorder the terms: -0.01020408164 + x = -0.285896443 Solving -0.01020408164 + x = -0.285896443 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 = -0.285896443 + 0.01020408164 Combine like terms: -0.01020408164 + 0.01020408164 = 0.00000000000 0.00000000000 + x = -0.285896443 + 0.01020408164 x = -0.285896443 + 0.01020408164 Combine like terms: -0.285896443 + 0.01020408164 = -0.27569236136 x = -0.27569236136 Simplifying x = -0.27569236136Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.29610052464, -0.27569236136}
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