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Simplifying 35x2 + -69x + 10 = 0 Reorder the terms: 10 + -69x + 35x2 = 0 Solving 10 + -69x + 35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. 0.2857142857 + -1.971428571x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + -1.971428571x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + -1.971428571x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + -1.971428571x + x2 = 0 + -0.2857142857 -1.971428571x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 -1.971428571x + x2 = -0.2857142857 The x term is -1.971428571x. Take half its coefficient (-0.9857142855). Square it (0.9716326526) and add it to both sides. Add '0.9716326526' to each side of the equation. -1.971428571x + 0.9716326526 + x2 = -0.2857142857 + 0.9716326526 Reorder the terms: 0.9716326526 + -1.971428571x + x2 = -0.2857142857 + 0.9716326526 Combine like terms: -0.2857142857 + 0.9716326526 = 0.6859183669 0.9716326526 + -1.971428571x + x2 = 0.6859183669 Factor a perfect square on the left side: (x + -0.9857142855)(x + -0.9857142855) = 0.6859183669 Calculate the square root of the right side: 0.828201888 Break this problem into two subproblems by setting (x + -0.9857142855) equal to 0.828201888 and -0.828201888.Subproblem 1
x + -0.9857142855 = 0.828201888 Simplifying x + -0.9857142855 = 0.828201888 Reorder the terms: -0.9857142855 + x = 0.828201888 Solving -0.9857142855 + x = 0.828201888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9857142855' to each side of the equation. -0.9857142855 + 0.9857142855 + x = 0.828201888 + 0.9857142855 Combine like terms: -0.9857142855 + 0.9857142855 = 0.0000000000 0.0000000000 + x = 0.828201888 + 0.9857142855 x = 0.828201888 + 0.9857142855 Combine like terms: 0.828201888 + 0.9857142855 = 1.8139161735 x = 1.8139161735 Simplifying x = 1.8139161735Subproblem 2
x + -0.9857142855 = -0.828201888 Simplifying x + -0.9857142855 = -0.828201888 Reorder the terms: -0.9857142855 + x = -0.828201888 Solving -0.9857142855 + x = -0.828201888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9857142855' to each side of the equation. -0.9857142855 + 0.9857142855 + x = -0.828201888 + 0.9857142855 Combine like terms: -0.9857142855 + 0.9857142855 = 0.0000000000 0.0000000000 + x = -0.828201888 + 0.9857142855 x = -0.828201888 + 0.9857142855 Combine like terms: -0.828201888 + 0.9857142855 = 0.1575123975 x = 0.1575123975 Simplifying x = 0.1575123975Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8139161735, 0.1575123975}
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