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Simplifying 1.7x(x + 5) = 2.1x + 9.7 Reorder the terms: 1.7x(5 + x) = 2.1x + 9.7 (5 * 1.7x + x * 1.7x) = 2.1x + 9.7 (8.5x + 1.7x2) = 2.1x + 9.7 Reorder the terms: 8.5x + 1.7x2 = 9.7 + 2.1x Solving 8.5x + 1.7x2 = 9.7 + 2.1x Solving for variable 'x'. Reorder the terms: -9.7 + 8.5x + -2.1x + 1.7x2 = 9.7 + 2.1x + -9.7 + -2.1x Combine like terms: 8.5x + -2.1x = 6.4x -9.7 + 6.4x + 1.7x2 = 9.7 + 2.1x + -9.7 + -2.1x Reorder the terms: -9.7 + 6.4x + 1.7x2 = 9.7 + -9.7 + 2.1x + -2.1x Combine like terms: 9.7 + -9.7 = 0.0 -9.7 + 6.4x + 1.7x2 = 0.0 + 2.1x + -2.1x -9.7 + 6.4x + 1.7x2 = 2.1x + -2.1x Combine like terms: 2.1x + -2.1x = 0.0 -9.7 + 6.4x + 1.7x2 = 0.0 Begin completing the square. Divide all terms by 1.7 the coefficient of the squared term: Divide each side by '1.7'. -5.705882353 + 3.764705882x + x2 = 0 Move the constant term to the right: Add '5.705882353' to each side of the equation. -5.705882353 + 3.764705882x + 5.705882353 + x2 = 0 + 5.705882353 Reorder the terms: -5.705882353 + 5.705882353 + 3.764705882x + x2 = 0 + 5.705882353 Combine like terms: -5.705882353 + 5.705882353 = 0.000000000 0.000000000 + 3.764705882x + x2 = 0 + 5.705882353 3.764705882x + x2 = 0 + 5.705882353 Combine like terms: 0 + 5.705882353 = 5.705882353 3.764705882x + x2 = 5.705882353 The x term is 3.764705882x. Take half its coefficient (1.882352941). Square it (3.543252594) and add it to both sides. Add '3.543252594' to each side of the equation. 3.764705882x + 3.543252594 + x2 = 5.705882353 + 3.543252594 Reorder the terms: 3.543252594 + 3.764705882x + x2 = 5.705882353 + 3.543252594 Combine like terms: 5.705882353 + 3.543252594 = 9.249134947 3.543252594 + 3.764705882x + x2 = 9.249134947 Factor a perfect square on the left side: (x + 1.882352941)(x + 1.882352941) = 9.249134947 Calculate the square root of the right side: 3.041239048 Break this problem into two subproblems by setting (x + 1.882352941) equal to 3.041239048 and -3.041239048.Subproblem 1
x + 1.882352941 = 3.041239048 Simplifying x + 1.882352941 = 3.041239048 Reorder the terms: 1.882352941 + x = 3.041239048 Solving 1.882352941 + x = 3.041239048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.882352941' to each side of the equation. 1.882352941 + -1.882352941 + x = 3.041239048 + -1.882352941 Combine like terms: 1.882352941 + -1.882352941 = 0.000000000 0.000000000 + x = 3.041239048 + -1.882352941 x = 3.041239048 + -1.882352941 Combine like terms: 3.041239048 + -1.882352941 = 1.158886107 x = 1.158886107 Simplifying x = 1.158886107Subproblem 2
x + 1.882352941 = -3.041239048 Simplifying x + 1.882352941 = -3.041239048 Reorder the terms: 1.882352941 + x = -3.041239048 Solving 1.882352941 + x = -3.041239048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.882352941' to each side of the equation. 1.882352941 + -1.882352941 + x = -3.041239048 + -1.882352941 Combine like terms: 1.882352941 + -1.882352941 = 0.000000000 0.000000000 + x = -3.041239048 + -1.882352941 x = -3.041239048 + -1.882352941 Combine like terms: -3.041239048 + -1.882352941 = -4.923591989 x = -4.923591989 Simplifying x = -4.923591989Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.158886107, -4.923591989}
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