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Simplifying 5x2 + 172x + -160 = 0 Reorder the terms: -160 + 172x + 5x2 = 0 Solving -160 + 172x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -32 + 34.4x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + 34.4x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 34.4x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 34.4x + x2 = 0 + 32 34.4x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 34.4x + x2 = 32 The x term is 34.4x. Take half its coefficient (17.2). Square it (295.84) and add it to both sides. Add '295.84' to each side of the equation. 34.4x + 295.84 + x2 = 32 + 295.84 Reorder the terms: 295.84 + 34.4x + x2 = 32 + 295.84 Combine like terms: 32 + 295.84 = 327.84 295.84 + 34.4x + x2 = 327.84 Factor a perfect square on the left side: (x + 17.2)(x + 17.2) = 327.84 Calculate the square root of the right side: 18.106352476 Break this problem into two subproblems by setting (x + 17.2) equal to 18.106352476 and -18.106352476.Subproblem 1
x + 17.2 = 18.106352476 Simplifying x + 17.2 = 18.106352476 Reorder the terms: 17.2 + x = 18.106352476 Solving 17.2 + x = 18.106352476 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.2' to each side of the equation. 17.2 + -17.2 + x = 18.106352476 + -17.2 Combine like terms: 17.2 + -17.2 = 0.0 0.0 + x = 18.106352476 + -17.2 x = 18.106352476 + -17.2 Combine like terms: 18.106352476 + -17.2 = 0.906352476 x = 0.906352476 Simplifying x = 0.906352476Subproblem 2
x + 17.2 = -18.106352476 Simplifying x + 17.2 = -18.106352476 Reorder the terms: 17.2 + x = -18.106352476 Solving 17.2 + x = -18.106352476 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.2' to each side of the equation. 17.2 + -17.2 + x = -18.106352476 + -17.2 Combine like terms: 17.2 + -17.2 = 0.0 0.0 + x = -18.106352476 + -17.2 x = -18.106352476 + -17.2 Combine like terms: -18.106352476 + -17.2 = -35.306352476 x = -35.306352476 Simplifying x = -35.306352476Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.906352476, -35.306352476}
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