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Simplifying -314.019418x2 + 24673.20799626468x + 1 = 0 Reorder the terms: 1 + 24673.20799626468x + -314.019418x2 = 0 Solving 1 + 24673.20799626468x + -314.019418x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -314.019418 the coefficient of the squared term: Divide each side by '-314.019418'. -0.003184516443 + -78.57223656x + x2 = 0 Move the constant term to the right: Add '0.003184516443' to each side of the equation. -0.003184516443 + -78.57223656x + 0.003184516443 + x2 = 0 + 0.003184516443 Reorder the terms: -0.003184516443 + 0.003184516443 + -78.57223656x + x2 = 0 + 0.003184516443 Combine like terms: -0.003184516443 + 0.003184516443 = 0.000000000000 0.000000000000 + -78.57223656x + x2 = 0 + 0.003184516443 -78.57223656x + x2 = 0 + 0.003184516443 Combine like terms: 0 + 0.003184516443 = 0.003184516443 -78.57223656x + x2 = 0.003184516443 The x term is -78.57223656x. Take half its coefficient (-39.28611828). Square it (1543.399090) and add it to both sides. Add '1543.399090' to each side of the equation. -78.57223656x + 1543.399090 + x2 = 0.003184516443 + 1543.399090 Reorder the terms: 1543.399090 + -78.57223656x + x2 = 0.003184516443 + 1543.399090 Combine like terms: 0.003184516443 + 1543.399090 = 1543.402274516443 1543.399090 + -78.57223656x + x2 = 1543.402274516443 Factor a perfect square on the left side: (x + -39.28611828)(x + -39.28611828) = 1543.402274516443 Calculate the square root of the right side: 39.286158816 Break this problem into two subproblems by setting (x + -39.28611828) equal to 39.286158816 and -39.286158816.Subproblem 1
x + -39.28611828 = 39.286158816 Simplifying x + -39.28611828 = 39.286158816 Reorder the terms: -39.28611828 + x = 39.286158816 Solving -39.28611828 + x = 39.286158816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '39.28611828' to each side of the equation. -39.28611828 + 39.28611828 + x = 39.286158816 + 39.28611828 Combine like terms: -39.28611828 + 39.28611828 = 0.00000000 0.00000000 + x = 39.286158816 + 39.28611828 x = 39.286158816 + 39.28611828 Combine like terms: 39.286158816 + 39.28611828 = 78.572277096 x = 78.572277096 Simplifying x = 78.572277096Subproblem 2
x + -39.28611828 = -39.286158816 Simplifying x + -39.28611828 = -39.286158816 Reorder the terms: -39.28611828 + x = -39.286158816 Solving -39.28611828 + x = -39.286158816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '39.28611828' to each side of the equation. -39.28611828 + 39.28611828 + x = -39.286158816 + 39.28611828 Combine like terms: -39.28611828 + 39.28611828 = 0.00000000 0.00000000 + x = -39.286158816 + 39.28611828 x = -39.286158816 + 39.28611828 Combine like terms: -39.286158816 + 39.28611828 = -0.000040536 x = -0.000040536 Simplifying x = -0.000040536Solution
The solution to the problem is based on the solutions from the subproblems. x = {78.572277096, -0.000040536}
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