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Simplifying 0.05x2 + -16.9x = 34 Reorder the terms: -16.9x + 0.05x2 = 34 Solving -16.9x + 0.05x2 = 34 Solving for variable 'x'. Reorder the terms: -34 + -16.9x + 0.05x2 = 34 + -34 Combine like terms: 34 + -34 = 0 -34 + -16.9x + 0.05x2 = 0 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 = 340 x = 340 Simplifying x = 340Subproblem 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 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {340, -2}
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