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Simplifying 8.5x2 + 29.2x + -162 = 0 Reorder the terms: -162 + 29.2x + 8.5x2 = 0 Solving -162 + 29.2x + 8.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8.5 the coefficient of the squared term: Divide each side by '8.5'. -19.05882353 + 3.435294118x + x2 = 0 Move the constant term to the right: Add '19.05882353' to each side of the equation. -19.05882353 + 3.435294118x + 19.05882353 + x2 = 0 + 19.05882353 Reorder the terms: -19.05882353 + 19.05882353 + 3.435294118x + x2 = 0 + 19.05882353 Combine like terms: -19.05882353 + 19.05882353 = 0.00000000 0.00000000 + 3.435294118x + x2 = 0 + 19.05882353 3.435294118x + x2 = 0 + 19.05882353 Combine like terms: 0 + 19.05882353 = 19.05882353 3.435294118x + x2 = 19.05882353 The x term is 3.435294118x. Take half its coefficient (1.717647059). Square it (2.950311419) and add it to both sides. Add '2.950311419' to each side of the equation. 3.435294118x + 2.950311419 + x2 = 19.05882353 + 2.950311419 Reorder the terms: 2.950311419 + 3.435294118x + x2 = 19.05882353 + 2.950311419 Combine like terms: 19.05882353 + 2.950311419 = 22.009134949 2.950311419 + 3.435294118x + x2 = 22.009134949 Factor a perfect square on the left side: (x + 1.717647059)(x + 1.717647059) = 22.009134949 Calculate the square root of the right side: 4.691389448 Break this problem into two subproblems by setting (x + 1.717647059) equal to 4.691389448 and -4.691389448.Subproblem 1
x + 1.717647059 = 4.691389448 Simplifying x + 1.717647059 = 4.691389448 Reorder the terms: 1.717647059 + x = 4.691389448 Solving 1.717647059 + x = 4.691389448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.717647059' to each side of the equation. 1.717647059 + -1.717647059 + x = 4.691389448 + -1.717647059 Combine like terms: 1.717647059 + -1.717647059 = 0.000000000 0.000000000 + x = 4.691389448 + -1.717647059 x = 4.691389448 + -1.717647059 Combine like terms: 4.691389448 + -1.717647059 = 2.973742389 x = 2.973742389 Simplifying x = 2.973742389Subproblem 2
x + 1.717647059 = -4.691389448 Simplifying x + 1.717647059 = -4.691389448 Reorder the terms: 1.717647059 + x = -4.691389448 Solving 1.717647059 + x = -4.691389448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.717647059' to each side of the equation. 1.717647059 + -1.717647059 + x = -4.691389448 + -1.717647059 Combine like terms: 1.717647059 + -1.717647059 = 0.000000000 0.000000000 + x = -4.691389448 + -1.717647059 x = -4.691389448 + -1.717647059 Combine like terms: -4.691389448 + -1.717647059 = -6.409036507 x = -6.409036507 Simplifying x = -6.409036507Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.973742389, -6.409036507}
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