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Simplifying 7x2 + 96x + 140 = 0 Reorder the terms: 140 + 96x + 7x2 = 0 Solving 140 + 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'. 20 + 13.71428571x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + 13.71428571x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 13.71428571x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 13.71428571x + x2 = 0 + -20 13.71428571x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 13.71428571x + x2 = -20 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 = -20 + 47.02040813 Reorder the terms: 47.02040813 + 13.71428571x + x2 = -20 + 47.02040813 Combine like terms: -20 + 47.02040813 = 27.02040813 47.02040813 + 13.71428571x + x2 = 27.02040813 Factor a perfect square on the left side: (x + 6.857142855)(x + 6.857142855) = 27.02040813 Calculate the square root of the right side: 5.198115825 Break this problem into two subproblems by setting (x + 6.857142855) equal to 5.198115825 and -5.198115825.Subproblem 1
x + 6.857142855 = 5.198115825 Simplifying x + 6.857142855 = 5.198115825 Reorder the terms: 6.857142855 + x = 5.198115825 Solving 6.857142855 + x = 5.198115825 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 = 5.198115825 + -6.857142855 Combine like terms: 6.857142855 + -6.857142855 = 0.000000000 0.000000000 + x = 5.198115825 + -6.857142855 x = 5.198115825 + -6.857142855 Combine like terms: 5.198115825 + -6.857142855 = -1.65902703 x = -1.65902703 Simplifying x = -1.65902703Subproblem 2
x + 6.857142855 = -5.198115825 Simplifying x + 6.857142855 = -5.198115825 Reorder the terms: 6.857142855 + x = -5.198115825 Solving 6.857142855 + x = -5.198115825 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 = -5.198115825 + -6.857142855 Combine like terms: 6.857142855 + -6.857142855 = 0.000000000 0.000000000 + x = -5.198115825 + -6.857142855 x = -5.198115825 + -6.857142855 Combine like terms: -5.198115825 + -6.857142855 = -12.05525868 x = -12.05525868 Simplifying x = -12.05525868Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.65902703, -12.05525868}
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