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Simplifying 35x2 + -69x + 5 = 0 Reorder the terms: 5 + -69x + 35x2 = 0 Solving 5 + -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'. 0.1428571429 + -1.971428571x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + -1.971428571x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + -1.971428571x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + -1.971428571x + x2 = 0 + -0.1428571429 -1.971428571x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 -1.971428571x + x2 = -0.1428571429 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 = -0.1428571429 + 0.9716326526 Reorder the terms: 0.9716326526 + -1.971428571x + x2 = -0.1428571429 + 0.9716326526 Combine like terms: -0.1428571429 + 0.9716326526 = 0.8287755097 0.9716326526 + -1.971428571x + x2 = 0.8287755097 Factor a perfect square on the left side: (x + -0.9857142855)(x + -0.9857142855) = 0.8287755097 Calculate the square root of the right side: 0.910371084 Break this problem into two subproblems by setting (x + -0.9857142855) equal to 0.910371084 and -0.910371084.Subproblem 1
x + -0.9857142855 = 0.910371084 Simplifying x + -0.9857142855 = 0.910371084 Reorder the terms: -0.9857142855 + x = 0.910371084 Solving -0.9857142855 + x = 0.910371084 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 = 0.910371084 + 0.9857142855 Combine like terms: -0.9857142855 + 0.9857142855 = 0.0000000000 0.0000000000 + x = 0.910371084 + 0.9857142855 x = 0.910371084 + 0.9857142855 Combine like terms: 0.910371084 + 0.9857142855 = 1.8960853695 x = 1.8960853695 Simplifying x = 1.8960853695Subproblem 2
x + -0.9857142855 = -0.910371084 Simplifying x + -0.9857142855 = -0.910371084 Reorder the terms: -0.9857142855 + x = -0.910371084 Solving -0.9857142855 + x = -0.910371084 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 = -0.910371084 + 0.9857142855 Combine like terms: -0.9857142855 + 0.9857142855 = 0.0000000000 0.0000000000 + x = -0.910371084 + 0.9857142855 x = -0.910371084 + 0.9857142855 Combine like terms: -0.910371084 + 0.9857142855 = 0.0753432015 x = 0.0753432015 Simplifying x = 0.0753432015Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8960853695, 0.0753432015}
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