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Simplifying 34 = 0.05x2 + 16.9x Reorder the terms: 34 = 16.9x + 0.05x2 Solving 34 = 16.9x + 0.05x2 Solving for variable 'x'. Reorder the terms: 34 + -16.9x + -0.05x2 = 16.9x + -16.9x + 0.05x2 + -0.05x2 Combine like terms: 16.9x + -16.9x = 0.0 34 + -16.9x + -0.05x2 = 0.0 + 0.05x2 + -0.05x2 34 + -16.9x + -0.05x2 = 0.05x2 + -0.05x2 Combine like terms: 0.05x2 + -0.05x2 = 0.00 34 + -16.9x + -0.05x2 = 0.00 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -680 + 338x + x2 = 0 Move the constant term to the right: Add '680' to each side of the equation. -680 + 338x + 680 + x2 = 0 + 680 Reorder the terms: -680 + 680 + 338x + x2 = 0 + 680 Combine like terms: -680 + 680 = 0 0 + 338x + x2 = 0 + 680 338x + x2 = 0 + 680 Combine like terms: 0 + 680 = 680 338x + x2 = 680 The x term is 338x. Take half its coefficient (169). Square it (28561) and add it to both sides. Add '28561' to each side of the equation. 338x + 28561 + x2 = 680 + 28561 Reorder the terms: 28561 + 338x + x2 = 680 + 28561 Combine like terms: 680 + 28561 = 29241 28561 + 338x + x2 = 29241 Factor a perfect square on the left side: (x + 169)(x + 169) = 29241 Calculate the square root of the right side: 171 Break this problem into two subproblems by setting (x + 169) equal to 171 and -171.Subproblem 1
x + 169 = 171 Simplifying x + 169 = 171 Reorder the terms: 169 + x = 171 Solving 169 + x = 171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-169' to each side of the equation. 169 + -169 + x = 171 + -169 Combine like terms: 169 + -169 = 0 0 + x = 171 + -169 x = 171 + -169 Combine like terms: 171 + -169 = 2 x = 2 Simplifying x = 2Subproblem 2
x + 169 = -171 Simplifying x + 169 = -171 Reorder the terms: 169 + x = -171 Solving 169 + x = -171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-169' to each side of the equation. 169 + -169 + x = -171 + -169 Combine like terms: 169 + -169 = 0 0 + x = -171 + -169 x = -171 + -169 Combine like terms: -171 + -169 = -340 x = -340 Simplifying x = -340Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, -340}
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