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Simplifying 14x2 + -192x + 64 = 0 Reorder the terms: 64 + -192x + 14x2 = 0 Solving 64 + -192x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(32 + -96x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(32 + -96x + 7x2)' equal to zero and attempt to solve: Simplifying 32 + -96x + 7x2 = 0 Solving 32 + -96x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 4.571428571 + -13.71428571x + x2 = 0 Move the constant term to the right: Add '-4.571428571' to each side of the equation. 4.571428571 + -13.71428571x + -4.571428571 + x2 = 0 + -4.571428571 Reorder the terms: 4.571428571 + -4.571428571 + -13.71428571x + x2 = 0 + -4.571428571 Combine like terms: 4.571428571 + -4.571428571 = 0.000000000 0.000000000 + -13.71428571x + x2 = 0 + -4.571428571 -13.71428571x + x2 = 0 + -4.571428571 Combine like terms: 0 + -4.571428571 = -4.571428571 -13.71428571x + x2 = -4.571428571 The x term is -13.71428571x. Take half its coefficient (-6.857142855). Square it (47.02040813) and add it to both sides. Add '47.02040813' to each side of the equation. -13.71428571x + 47.02040813 + x2 = -4.571428571 + 47.02040813 Reorder the terms: 47.02040813 + -13.71428571x + x2 = -4.571428571 + 47.02040813 Combine like terms: -4.571428571 + 47.02040813 = 42.448979559 47.02040813 + -13.71428571x + x2 = 42.448979559 Factor a perfect square on the left side: (x + -6.857142855)(x + -6.857142855) = 42.448979559 Calculate the square root of the right side: 6.515288141 Break this problem into two subproblems by setting (x + -6.857142855) equal to 6.515288141 and -6.515288141.Subproblem 1
x + -6.857142855 = 6.515288141 Simplifying x + -6.857142855 = 6.515288141 Reorder the terms: -6.857142855 + x = 6.515288141 Solving -6.857142855 + x = 6.515288141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.857142855' to each side of the equation. -6.857142855 + 6.857142855 + x = 6.515288141 + 6.857142855 Combine like terms: -6.857142855 + 6.857142855 = 0.000000000 0.000000000 + x = 6.515288141 + 6.857142855 x = 6.515288141 + 6.857142855 Combine like terms: 6.515288141 + 6.857142855 = 13.372430996 x = 13.372430996 Simplifying x = 13.372430996Subproblem 2
x + -6.857142855 = -6.515288141 Simplifying x + -6.857142855 = -6.515288141 Reorder the terms: -6.857142855 + x = -6.515288141 Solving -6.857142855 + x = -6.515288141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.857142855' to each side of the equation. -6.857142855 + 6.857142855 + x = -6.515288141 + 6.857142855 Combine like terms: -6.857142855 + 6.857142855 = 0.000000000 0.000000000 + x = -6.515288141 + 6.857142855 x = -6.515288141 + 6.857142855 Combine like terms: -6.515288141 + 6.857142855 = 0.341854714 x = 0.341854714 Simplifying x = 0.341854714Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.372430996, 0.341854714}Solution
x = {13.372430996, 0.341854714}
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