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Simplifying 21x2 + 17x + 3 = 0 Reorder the terms: 3 + 17x + 21x2 = 0 Solving 3 + 17x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.1428571429 + 0.8095238095x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 0.8095238095x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 0.8095238095x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 0.8095238095x + x2 = 0 + -0.1428571429 0.8095238095x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 0.8095238095x + x2 = -0.1428571429 The x term is 0.8095238095x. Take half its coefficient (0.4047619048). Square it (0.1638321996) and add it to both sides. Add '0.1638321996' to each side of the equation. 0.8095238095x + 0.1638321996 + x2 = -0.1428571429 + 0.1638321996 Reorder the terms: 0.1638321996 + 0.8095238095x + x2 = -0.1428571429 + 0.1638321996 Combine like terms: -0.1428571429 + 0.1638321996 = 0.0209750567 0.1638321996 + 0.8095238095x + x2 = 0.0209750567 Factor a perfect square on the left side: (x + 0.4047619048)(x + 0.4047619048) = 0.0209750567 Calculate the square root of the right side: 0.144827679 Break this problem into two subproblems by setting (x + 0.4047619048) equal to 0.144827679 and -0.144827679.Subproblem 1
x + 0.4047619048 = 0.144827679 Simplifying x + 0.4047619048 = 0.144827679 Reorder the terms: 0.4047619048 + x = 0.144827679 Solving 0.4047619048 + x = 0.144827679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4047619048' to each side of the equation. 0.4047619048 + -0.4047619048 + x = 0.144827679 + -0.4047619048 Combine like terms: 0.4047619048 + -0.4047619048 = 0.0000000000 0.0000000000 + x = 0.144827679 + -0.4047619048 x = 0.144827679 + -0.4047619048 Combine like terms: 0.144827679 + -0.4047619048 = -0.2599342258 x = -0.2599342258 Simplifying x = -0.2599342258Subproblem 2
x + 0.4047619048 = -0.144827679 Simplifying x + 0.4047619048 = -0.144827679 Reorder the terms: 0.4047619048 + x = -0.144827679 Solving 0.4047619048 + x = -0.144827679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4047619048' to each side of the equation. 0.4047619048 + -0.4047619048 + x = -0.144827679 + -0.4047619048 Combine like terms: 0.4047619048 + -0.4047619048 = 0.0000000000 0.0000000000 + x = -0.144827679 + -0.4047619048 x = -0.144827679 + -0.4047619048 Combine like terms: -0.144827679 + -0.4047619048 = -0.5495895838 x = -0.5495895838 Simplifying x = -0.5495895838Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2599342258, -0.5495895838}
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