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Simplifying 196x2 + -56x + 4 = 8 Reorder the terms: 4 + -56x + 196x2 = 8 Solving 4 + -56x + 196x2 = 8 Solving for variable 'x'. Reorder the terms: 4 + -8 + -56x + 196x2 = 8 + -8 Combine like terms: 4 + -8 = -4 -4 + -56x + 196x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -4 + -56x + 196x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + -14x + 49x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -14x + 49x2)' equal to zero and attempt to solve: Simplifying -1 + -14x + 49x2 = 0 Solving -1 + -14x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.02040816327 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.02040816327' to each side of the equation. -0.02040816327 + -0.2857142857x + 0.02040816327 + x2 = 0 + 0.02040816327 Reorder the terms: -0.02040816327 + 0.02040816327 + -0.2857142857x + x2 = 0 + 0.02040816327 Combine like terms: -0.02040816327 + 0.02040816327 = 0.00000000000 0.00000000000 + -0.2857142857x + x2 = 0 + 0.02040816327 -0.2857142857x + x2 = 0 + 0.02040816327 Combine like terms: 0 + 0.02040816327 = 0.02040816327 -0.2857142857x + x2 = 0.02040816327 The x term is -0.2857142857x. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x + 0.02040816328 + x2 = 0.02040816327 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 0.02040816327 + 0.02040816328 Combine like terms: 0.02040816327 + 0.02040816328 = 0.04081632655 0.02040816328 + -0.2857142857x + x2 = 0.04081632655 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 0.04081632655 Calculate the square root of the right side: 0.202030509 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 0.202030509 and -0.202030509.Subproblem 1
x + -0.1428571429 = 0.202030509 Simplifying x + -0.1428571429 = 0.202030509 Reorder the terms: -0.1428571429 + x = 0.202030509 Solving -0.1428571429 + x = 0.202030509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 0.202030509 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 0.202030509 + 0.1428571429 x = 0.202030509 + 0.1428571429 Combine like terms: 0.202030509 + 0.1428571429 = 0.3448876519 x = 0.3448876519 Simplifying x = 0.3448876519Subproblem 2
x + -0.1428571429 = -0.202030509 Simplifying x + -0.1428571429 = -0.202030509 Reorder the terms: -0.1428571429 + x = -0.202030509 Solving -0.1428571429 + x = -0.202030509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -0.202030509 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -0.202030509 + 0.1428571429 x = -0.202030509 + 0.1428571429 Combine like terms: -0.202030509 + 0.1428571429 = -0.0591733661 x = -0.0591733661 Simplifying x = -0.0591733661Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3448876519, -0.0591733661}Solution
x = {0.3448876519, -0.0591733661}
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