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Simplifying 34x2 + 42x + -441 = 0 Reorder the terms: -441 + 42x + 34x2 = 0 Solving -441 + 42x + 34x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 34 the coefficient of the squared term: Divide each side by '34'. -12.97058824 + 1.235294118x + x2 = 0 Move the constant term to the right: Add '12.97058824' to each side of the equation. -12.97058824 + 1.235294118x + 12.97058824 + x2 = 0 + 12.97058824 Reorder the terms: -12.97058824 + 12.97058824 + 1.235294118x + x2 = 0 + 12.97058824 Combine like terms: -12.97058824 + 12.97058824 = 0.00000000 0.00000000 + 1.235294118x + x2 = 0 + 12.97058824 1.235294118x + x2 = 0 + 12.97058824 Combine like terms: 0 + 12.97058824 = 12.97058824 1.235294118x + x2 = 12.97058824 The x term is 1.235294118x. Take half its coefficient (0.617647059). Square it (0.3814878895) and add it to both sides. Add '0.3814878895' to each side of the equation. 1.235294118x + 0.3814878895 + x2 = 12.97058824 + 0.3814878895 Reorder the terms: 0.3814878895 + 1.235294118x + x2 = 12.97058824 + 0.3814878895 Combine like terms: 12.97058824 + 0.3814878895 = 13.3520761295 0.3814878895 + 1.235294118x + x2 = 13.3520761295 Factor a perfect square on the left side: (x + 0.617647059)(x + 0.617647059) = 13.3520761295 Calculate the square root of the right side: 3.654049278 Break this problem into two subproblems by setting (x + 0.617647059) equal to 3.654049278 and -3.654049278.Subproblem 1
x + 0.617647059 = 3.654049278 Simplifying x + 0.617647059 = 3.654049278 Reorder the terms: 0.617647059 + x = 3.654049278 Solving 0.617647059 + x = 3.654049278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.617647059' to each side of the equation. 0.617647059 + -0.617647059 + x = 3.654049278 + -0.617647059 Combine like terms: 0.617647059 + -0.617647059 = 0.000000000 0.000000000 + x = 3.654049278 + -0.617647059 x = 3.654049278 + -0.617647059 Combine like terms: 3.654049278 + -0.617647059 = 3.036402219 x = 3.036402219 Simplifying x = 3.036402219Subproblem 2
x + 0.617647059 = -3.654049278 Simplifying x + 0.617647059 = -3.654049278 Reorder the terms: 0.617647059 + x = -3.654049278 Solving 0.617647059 + x = -3.654049278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.617647059' to each side of the equation. 0.617647059 + -0.617647059 + x = -3.654049278 + -0.617647059 Combine like terms: 0.617647059 + -0.617647059 = 0.000000000 0.000000000 + x = -3.654049278 + -0.617647059 x = -3.654049278 + -0.617647059 Combine like terms: -3.654049278 + -0.617647059 = -4.271696337 x = -4.271696337 Simplifying x = -4.271696337Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.036402219, -4.271696337}
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