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Simplifying 11x2 + -3780x + -360 = 0 Reorder the terms: -360 + -3780x + 11x2 = 0 Solving -360 + -3780x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -32.72727273 + -343.6363636x + x2 = 0 Move the constant term to the right: Add '32.72727273' to each side of the equation. -32.72727273 + -343.6363636x + 32.72727273 + x2 = 0 + 32.72727273 Reorder the terms: -32.72727273 + 32.72727273 + -343.6363636x + x2 = 0 + 32.72727273 Combine like terms: -32.72727273 + 32.72727273 = 0.00000000 0.00000000 + -343.6363636x + x2 = 0 + 32.72727273 -343.6363636x + x2 = 0 + 32.72727273 Combine like terms: 0 + 32.72727273 = 32.72727273 -343.6363636x + x2 = 32.72727273 The x term is -343.6363636x. Take half its coefficient (-171.8181818). Square it (29521.48760) and add it to both sides. Add '29521.48760' to each side of the equation. -343.6363636x + 29521.48760 + x2 = 32.72727273 + 29521.48760 Reorder the terms: 29521.48760 + -343.6363636x + x2 = 32.72727273 + 29521.48760 Combine like terms: 32.72727273 + 29521.48760 = 29554.21487273 29521.48760 + -343.6363636x + x2 = 29554.21487273 Factor a perfect square on the left side: (x + -171.8181818)(x + -171.8181818) = 29554.21487273 Calculate the square root of the right side: 171.913393523 Break this problem into two subproblems by setting (x + -171.8181818) equal to 171.913393523 and -171.913393523.Subproblem 1
x + -171.8181818 = 171.913393523 Simplifying x + -171.8181818 = 171.913393523 Reorder the terms: -171.8181818 + x = 171.913393523 Solving -171.8181818 + x = 171.913393523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '171.8181818' to each side of the equation. -171.8181818 + 171.8181818 + x = 171.913393523 + 171.8181818 Combine like terms: -171.8181818 + 171.8181818 = 0.0000000 0.0000000 + x = 171.913393523 + 171.8181818 x = 171.913393523 + 171.8181818 Combine like terms: 171.913393523 + 171.8181818 = 343.731575323 x = 343.731575323 Simplifying x = 343.731575323Subproblem 2
x + -171.8181818 = -171.913393523 Simplifying x + -171.8181818 = -171.913393523 Reorder the terms: -171.8181818 + x = -171.913393523 Solving -171.8181818 + x = -171.913393523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '171.8181818' to each side of the equation. -171.8181818 + 171.8181818 + x = -171.913393523 + 171.8181818 Combine like terms: -171.8181818 + 171.8181818 = 0.0000000 0.0000000 + x = -171.913393523 + 171.8181818 x = -171.913393523 + 171.8181818 Combine like terms: -171.913393523 + 171.8181818 = -0.095211723 x = -0.095211723 Simplifying x = -0.095211723Solution
The solution to the problem is based on the solutions from the subproblems. x = {343.731575323, -0.095211723}
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