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Simplifying 7x2 + -96x + 28 = 0 Reorder the terms: 28 + -96x + 7x2 = 0 Solving 28 + -96x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 4 + -13.71428571x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -13.71428571x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -13.71428571x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -13.71428571x + x2 = 0 + -4 -13.71428571x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -13.71428571x + x2 = -4 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 + 47.02040813 Reorder the terms: 47.02040813 + -13.71428571x + x2 = -4 + 47.02040813 Combine like terms: -4 + 47.02040813 = 43.02040813 47.02040813 + -13.71428571x + x2 = 43.02040813 Factor a perfect square on the left side: (x + -6.857142855)(x + -6.857142855) = 43.02040813 Calculate the square root of the right side: 6.558994445 Break this problem into two subproblems by setting (x + -6.857142855) equal to 6.558994445 and -6.558994445.Subproblem 1
x + -6.857142855 = 6.558994445 Simplifying x + -6.857142855 = 6.558994445 Reorder the terms: -6.857142855 + x = 6.558994445 Solving -6.857142855 + x = 6.558994445 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 = 6.558994445 + 6.857142855 Combine like terms: -6.857142855 + 6.857142855 = 0.000000000 0.000000000 + x = 6.558994445 + 6.857142855 x = 6.558994445 + 6.857142855 Combine like terms: 6.558994445 + 6.857142855 = 13.4161373 x = 13.4161373 Simplifying x = 13.4161373Subproblem 2
x + -6.857142855 = -6.558994445 Simplifying x + -6.857142855 = -6.558994445 Reorder the terms: -6.857142855 + x = -6.558994445 Solving -6.857142855 + x = -6.558994445 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 = -6.558994445 + 6.857142855 Combine like terms: -6.857142855 + 6.857142855 = 0.000000000 0.000000000 + x = -6.558994445 + 6.857142855 x = -6.558994445 + 6.857142855 Combine like terms: -6.558994445 + 6.857142855 = 0.29814841 x = 0.29814841 Simplifying x = 0.29814841Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.4161373, 0.29814841}
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