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Simplifying 7x2 + 96x + -175 = 0 Reorder the terms: -175 + 96x + 7x2 = 0 Solving -175 + 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'. -25 + 13.71428571x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 13.71428571x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 13.71428571x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 13.71428571x + x2 = 0 + 25 13.71428571x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 13.71428571x + x2 = 25 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 = 25 + 47.02040813 Reorder the terms: 47.02040813 + 13.71428571x + x2 = 25 + 47.02040813 Combine like terms: 25 + 47.02040813 = 72.02040813 47.02040813 + 13.71428571x + x2 = 72.02040813 Factor a perfect square on the left side: (x + 6.857142855)(x + 6.857142855) = 72.02040813 Calculate the square root of the right side: 8.48648385 Break this problem into two subproblems by setting (x + 6.857142855) equal to 8.48648385 and -8.48648385.Subproblem 1
x + 6.857142855 = 8.48648385 Simplifying x + 6.857142855 = 8.48648385 Reorder the terms: 6.857142855 + x = 8.48648385 Solving 6.857142855 + x = 8.48648385 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 = 8.48648385 + -6.857142855 Combine like terms: 6.857142855 + -6.857142855 = 0.000000000 0.000000000 + x = 8.48648385 + -6.857142855 x = 8.48648385 + -6.857142855 Combine like terms: 8.48648385 + -6.857142855 = 1.629340995 x = 1.629340995 Simplifying x = 1.629340995Subproblem 2
x + 6.857142855 = -8.48648385 Simplifying x + 6.857142855 = -8.48648385 Reorder the terms: 6.857142855 + x = -8.48648385 Solving 6.857142855 + x = -8.48648385 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 = -8.48648385 + -6.857142855 Combine like terms: 6.857142855 + -6.857142855 = 0.000000000 0.000000000 + x = -8.48648385 + -6.857142855 x = -8.48648385 + -6.857142855 Combine like terms: -8.48648385 + -6.857142855 = -15.343626705 x = -15.343626705 Simplifying x = -15.343626705Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.629340995, -15.343626705}
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