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Simplifying 4x2 + 340x + -169 = 0 Reorder the terms: -169 + 340x + 4x2 = 0 Solving -169 + 340x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -42.25 + 85x + x2 = 0 Move the constant term to the right: Add '42.25' to each side of the equation. -42.25 + 85x + 42.25 + x2 = 0 + 42.25 Reorder the terms: -42.25 + 42.25 + 85x + x2 = 0 + 42.25 Combine like terms: -42.25 + 42.25 = 0.00 0.00 + 85x + x2 = 0 + 42.25 85x + x2 = 0 + 42.25 Combine like terms: 0 + 42.25 = 42.25 85x + x2 = 42.25 The x term is 85x. Take half its coefficient (42.5). Square it (1806.25) and add it to both sides. Add '1806.25' to each side of the equation. 85x + 1806.25 + x2 = 42.25 + 1806.25 Reorder the terms: 1806.25 + 85x + x2 = 42.25 + 1806.25 Combine like terms: 42.25 + 1806.25 = 1848.5 1806.25 + 85x + x2 = 1848.5 Factor a perfect square on the left side: (x + 42.5)(x + 42.5) = 1848.5 Calculate the square root of the right side: 42.994185653 Break this problem into two subproblems by setting (x + 42.5) equal to 42.994185653 and -42.994185653.Subproblem 1
x + 42.5 = 42.994185653 Simplifying x + 42.5 = 42.994185653 Reorder the terms: 42.5 + x = 42.994185653 Solving 42.5 + x = 42.994185653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42.5' to each side of the equation. 42.5 + -42.5 + x = 42.994185653 + -42.5 Combine like terms: 42.5 + -42.5 = 0.0 0.0 + x = 42.994185653 + -42.5 x = 42.994185653 + -42.5 Combine like terms: 42.994185653 + -42.5 = 0.494185653 x = 0.494185653 Simplifying x = 0.494185653Subproblem 2
x + 42.5 = -42.994185653 Simplifying x + 42.5 = -42.994185653 Reorder the terms: 42.5 + x = -42.994185653 Solving 42.5 + x = -42.994185653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42.5' to each side of the equation. 42.5 + -42.5 + x = -42.994185653 + -42.5 Combine like terms: 42.5 + -42.5 = 0.0 0.0 + x = -42.994185653 + -42.5 x = -42.994185653 + -42.5 Combine like terms: -42.994185653 + -42.5 = -85.494185653 x = -85.494185653 Simplifying x = -85.494185653Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.494185653, -85.494185653}
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