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Simplifying 3888.21 = 12.117x2 + -233.406x + 1765.675 Reorder the terms: 3888.21 = 1765.675 + -233.406x + 12.117x2 Solving 3888.21 = 1765.675 + -233.406x + 12.117x2 Solving for variable 'x'. Combine like terms: 3888.21 + -1765.675 = 2122.535 2122.535 + 233.406x + -12.117x2 = 1765.675 + -233.406x + 12.117x2 + -1765.675 + 233.406x + -12.117x2 Reorder the terms: 2122.535 + 233.406x + -12.117x2 = 1765.675 + -1765.675 + -233.406x + 233.406x + 12.117x2 + -12.117x2 Combine like terms: 1765.675 + -1765.675 = 0.000 2122.535 + 233.406x + -12.117x2 = 0.000 + -233.406x + 233.406x + 12.117x2 + -12.117x2 2122.535 + 233.406x + -12.117x2 = -233.406x + 233.406x + 12.117x2 + -12.117x2 Combine like terms: -233.406x + 233.406x = 0.000 2122.535 + 233.406x + -12.117x2 = 0.000 + 12.117x2 + -12.117x2 2122.535 + 233.406x + -12.117x2 = 12.117x2 + -12.117x2 Combine like terms: 12.117x2 + -12.117x2 = 0.000 2122.535 + 233.406x + -12.117x2 = 0.000 Begin completing the square. Divide all terms by -12.117 the coefficient of the squared term: Divide each side by '-12.117'. -175.1700091 + -19.26268878x + x2 = 0 Move the constant term to the right: Add '175.1700091' to each side of the equation. -175.1700091 + -19.26268878x + 175.1700091 + x2 = 0 + 175.1700091 Reorder the terms: -175.1700091 + 175.1700091 + -19.26268878x + x2 = 0 + 175.1700091 Combine like terms: -175.1700091 + 175.1700091 = 0.0000000 0.0000000 + -19.26268878x + x2 = 0 + 175.1700091 -19.26268878x + x2 = 0 + 175.1700091 Combine like terms: 0 + 175.1700091 = 175.1700091 -19.26268878x + x2 = 175.1700091 The x term is -19.26268878x. Take half its coefficient (-9.63134439). Square it (92.76279476) and add it to both sides. Add '92.76279476' to each side of the equation. -19.26268878x + 92.76279476 + x2 = 175.1700091 + 92.76279476 Reorder the terms: 92.76279476 + -19.26268878x + x2 = 175.1700091 + 92.76279476 Combine like terms: 175.1700091 + 92.76279476 = 267.93280386 92.76279476 + -19.26268878x + x2 = 267.93280386 Factor a perfect square on the left side: (x + -9.63134439)(x + -9.63134439) = 267.93280386 Calculate the square root of the right side: 16.368653086 Break this problem into two subproblems by setting (x + -9.63134439) equal to 16.368653086 and -16.368653086.Subproblem 1
x + -9.63134439 = 16.368653086 Simplifying x + -9.63134439 = 16.368653086 Reorder the terms: -9.63134439 + x = 16.368653086 Solving -9.63134439 + x = 16.368653086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.63134439' to each side of the equation. -9.63134439 + 9.63134439 + x = 16.368653086 + 9.63134439 Combine like terms: -9.63134439 + 9.63134439 = 0.00000000 0.00000000 + x = 16.368653086 + 9.63134439 x = 16.368653086 + 9.63134439 Combine like terms: 16.368653086 + 9.63134439 = 25.999997476 x = 25.999997476 Simplifying x = 25.999997476Subproblem 2
x + -9.63134439 = -16.368653086 Simplifying x + -9.63134439 = -16.368653086 Reorder the terms: -9.63134439 + x = -16.368653086 Solving -9.63134439 + x = -16.368653086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.63134439' to each side of the equation. -9.63134439 + 9.63134439 + x = -16.368653086 + 9.63134439 Combine like terms: -9.63134439 + 9.63134439 = 0.00000000 0.00000000 + x = -16.368653086 + 9.63134439 x = -16.368653086 + 9.63134439 Combine like terms: -16.368653086 + 9.63134439 = -6.737308696 x = -6.737308696 Simplifying x = -6.737308696Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.999997476, -6.737308696}
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