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Simplifying 35x2 + 10x + 1 = 9 Reorder the terms: 1 + 10x + 35x2 = 9 Solving 1 + 10x + 35x2 = 9 Solving for variable 'x'. Reorder the terms: 1 + -9 + 10x + 35x2 = 9 + -9 Combine like terms: 1 + -9 = -8 -8 + 10x + 35x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -8 + 10x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.2285714286 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.2285714286' to each side of the equation. -0.2285714286 + 0.2857142857x + 0.2285714286 + x2 = 0 + 0.2285714286 Reorder the terms: -0.2285714286 + 0.2285714286 + 0.2857142857x + x2 = 0 + 0.2285714286 Combine like terms: -0.2285714286 + 0.2285714286 = 0.0000000000 0.0000000000 + 0.2857142857x + x2 = 0 + 0.2285714286 0.2857142857x + x2 = 0 + 0.2285714286 Combine like terms: 0 + 0.2285714286 = 0.2285714286 0.2857142857x + x2 = 0.2285714286 The x term is 0.2857142857x. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857x + 0.02040816328 + x2 = 0.2285714286 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 0.2285714286 + 0.02040816328 Combine like terms: 0.2285714286 + 0.02040816328 = 0.24897959188 0.02040816328 + 0.2857142857x + x2 = 0.24897959188 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 0.24897959188 Calculate the square root of the right side: 0.498978549 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 0.498978549 and -0.498978549.Subproblem 1
x + 0.1428571429 = 0.498978549 Simplifying x + 0.1428571429 = 0.498978549 Reorder the terms: 0.1428571429 + x = 0.498978549 Solving 0.1428571429 + x = 0.498978549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = 0.498978549 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 0.498978549 + -0.1428571429 x = 0.498978549 + -0.1428571429 Combine like terms: 0.498978549 + -0.1428571429 = 0.3561214061 x = 0.3561214061 Simplifying x = 0.3561214061Subproblem 2
x + 0.1428571429 = -0.498978549 Simplifying x + 0.1428571429 = -0.498978549 Reorder the terms: 0.1428571429 + x = -0.498978549 Solving 0.1428571429 + x = -0.498978549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = -0.498978549 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -0.498978549 + -0.1428571429 x = -0.498978549 + -0.1428571429 Combine like terms: -0.498978549 + -0.1428571429 = -0.6418356919 x = -0.6418356919 Simplifying x = -0.6418356919Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3561214061, -0.6418356919}
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