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Simplifying 7x2 + -29x + -35 = 0 Reorder the terms: -35 + -29x + 7x2 = 0 Solving -35 + -29x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5 + -4.142857143x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -4.142857143x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -4.142857143x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4.142857143x + x2 = 0 + 5 -4.142857143x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -4.142857143x + x2 = 5 The x term is -4.142857143x. Take half its coefficient (-2.071428572). Square it (4.290816329) and add it to both sides. Add '4.290816329' to each side of the equation. -4.142857143x + 4.290816329 + x2 = 5 + 4.290816329 Reorder the terms: 4.290816329 + -4.142857143x + x2 = 5 + 4.290816329 Combine like terms: 5 + 4.290816329 = 9.290816329 4.290816329 + -4.142857143x + x2 = 9.290816329 Factor a perfect square on the left side: (x + -2.071428572)(x + -2.071428572) = 9.290816329 Calculate the square root of the right side: 3.048084042 Break this problem into two subproblems by setting (x + -2.071428572) equal to 3.048084042 and -3.048084042.Subproblem 1
x + -2.071428572 = 3.048084042 Simplifying x + -2.071428572 = 3.048084042 Reorder the terms: -2.071428572 + x = 3.048084042 Solving -2.071428572 + x = 3.048084042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.071428572' to each side of the equation. -2.071428572 + 2.071428572 + x = 3.048084042 + 2.071428572 Combine like terms: -2.071428572 + 2.071428572 = 0.000000000 0.000000000 + x = 3.048084042 + 2.071428572 x = 3.048084042 + 2.071428572 Combine like terms: 3.048084042 + 2.071428572 = 5.119512614 x = 5.119512614 Simplifying x = 5.119512614Subproblem 2
x + -2.071428572 = -3.048084042 Simplifying x + -2.071428572 = -3.048084042 Reorder the terms: -2.071428572 + x = -3.048084042 Solving -2.071428572 + x = -3.048084042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.071428572' to each side of the equation. -2.071428572 + 2.071428572 + x = -3.048084042 + 2.071428572 Combine like terms: -2.071428572 + 2.071428572 = 0.000000000 0.000000000 + x = -3.048084042 + 2.071428572 x = -3.048084042 + 2.071428572 Combine like terms: -3.048084042 + 2.071428572 = -0.97665547 x = -0.97665547 Simplifying x = -0.97665547Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.119512614, -0.97665547}
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