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Simplifying 35x2 + -69x + 12 = 0 Reorder the terms: 12 + -69x + 35x2 = 0 Solving 12 + -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'. 0.3428571429 + -1.971428571x + x2 = 0 Move the constant term to the right: Add '-0.3428571429' to each side of the equation. 0.3428571429 + -1.971428571x + -0.3428571429 + x2 = 0 + -0.3428571429 Reorder the terms: 0.3428571429 + -0.3428571429 + -1.971428571x + x2 = 0 + -0.3428571429 Combine like terms: 0.3428571429 + -0.3428571429 = 0.0000000000 0.0000000000 + -1.971428571x + x2 = 0 + -0.3428571429 -1.971428571x + x2 = 0 + -0.3428571429 Combine like terms: 0 + -0.3428571429 = -0.3428571429 -1.971428571x + x2 = -0.3428571429 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 = -0.3428571429 + 0.9716326526 Reorder the terms: 0.9716326526 + -1.971428571x + x2 = -0.3428571429 + 0.9716326526 Combine like terms: -0.3428571429 + 0.9716326526 = 0.6287755097 0.9716326526 + -1.971428571x + x2 = 0.6287755097 Factor a perfect square on the left side: (x + -0.9857142855)(x + -0.9857142855) = 0.6287755097 Calculate the square root of the right side: 0.792953662 Break this problem into two subproblems by setting (x + -0.9857142855) equal to 0.792953662 and -0.792953662.Subproblem 1
x + -0.9857142855 = 0.792953662 Simplifying x + -0.9857142855 = 0.792953662 Reorder the terms: -0.9857142855 + x = 0.792953662 Solving -0.9857142855 + x = 0.792953662 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 = 0.792953662 + 0.9857142855 Combine like terms: -0.9857142855 + 0.9857142855 = 0.0000000000 0.0000000000 + x = 0.792953662 + 0.9857142855 x = 0.792953662 + 0.9857142855 Combine like terms: 0.792953662 + 0.9857142855 = 1.7786679475 x = 1.7786679475 Simplifying x = 1.7786679475Subproblem 2
x + -0.9857142855 = -0.792953662 Simplifying x + -0.9857142855 = -0.792953662 Reorder the terms: -0.9857142855 + x = -0.792953662 Solving -0.9857142855 + x = -0.792953662 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 = -0.792953662 + 0.9857142855 Combine like terms: -0.9857142855 + 0.9857142855 = 0.0000000000 0.0000000000 + x = -0.792953662 + 0.9857142855 x = -0.792953662 + 0.9857142855 Combine like terms: -0.792953662 + 0.9857142855 = 0.1927606235 x = 0.1927606235 Simplifying x = 0.1927606235Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7786679475, 0.1927606235}
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