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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 = 1.3144897955 0.9716326526 + -1.971428571x + x2 = 1.3144897955 Factor a perfect square on the left side: (x + -0.9857142855)(x + -0.9857142855) = 1.3144897955 Calculate the square root of the right side: 1.146512013 Break this problem into two subproblems by setting (x + -0.9857142855) equal to 1.146512013 and -1.146512013.Subproblem 1
x + -0.9857142855 = 1.146512013 Simplifying x + -0.9857142855 = 1.146512013 Reorder the terms: -0.9857142855 + x = 1.146512013 Solving -0.9857142855 + x = 1.146512013 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 = 1.146512013 + 0.9857142855 Combine like terms: -0.9857142855 + 0.9857142855 = 0.0000000000 0.0000000000 + x = 1.146512013 + 0.9857142855 x = 1.146512013 + 0.9857142855 Combine like terms: 1.146512013 + 0.9857142855 = 2.1322262985 x = 2.1322262985 Simplifying x = 2.1322262985Subproblem 2
x + -0.9857142855 = -1.146512013 Simplifying x + -0.9857142855 = -1.146512013 Reorder the terms: -0.9857142855 + x = -1.146512013 Solving -0.9857142855 + x = -1.146512013 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 = -1.146512013 + 0.9857142855 Combine like terms: -0.9857142855 + 0.9857142855 = 0.0000000000 0.0000000000 + x = -1.146512013 + 0.9857142855 x = -1.146512013 + 0.9857142855 Combine like terms: -1.146512013 + 0.9857142855 = -0.1607977275 x = -0.1607977275 Simplifying x = -0.1607977275Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1322262985, -0.1607977275}
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