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Simplifying 575 = 1.36x2 + 27.8x + 304 Reorder the terms: 575 = 304 + 27.8x + 1.36x2 Solving 575 = 304 + 27.8x + 1.36x2 Solving for variable 'x'. Combine like terms: 575 + -304 = 271 271 + -27.8x + -1.36x2 = 304 + 27.8x + 1.36x2 + -304 + -27.8x + -1.36x2 Reorder the terms: 271 + -27.8x + -1.36x2 = 304 + -304 + 27.8x + -27.8x + 1.36x2 + -1.36x2 Combine like terms: 304 + -304 = 0 271 + -27.8x + -1.36x2 = 0 + 27.8x + -27.8x + 1.36x2 + -1.36x2 271 + -27.8x + -1.36x2 = 27.8x + -27.8x + 1.36x2 + -1.36x2 Combine like terms: 27.8x + -27.8x = 0.0 271 + -27.8x + -1.36x2 = 0.0 + 1.36x2 + -1.36x2 271 + -27.8x + -1.36x2 = 1.36x2 + -1.36x2 Combine like terms: 1.36x2 + -1.36x2 = 0.00 271 + -27.8x + -1.36x2 = 0.00 Begin completing the square. Divide all terms by -1.36 the coefficient of the squared term: Divide each side by '-1.36'. -199.2647059 + 20.44117647x + x2 = 0 Move the constant term to the right: Add '199.2647059' to each side of the equation. -199.2647059 + 20.44117647x + 199.2647059 + x2 = 0 + 199.2647059 Reorder the terms: -199.2647059 + 199.2647059 + 20.44117647x + x2 = 0 + 199.2647059 Combine like terms: -199.2647059 + 199.2647059 = 0.0000000 0.0000000 + 20.44117647x + x2 = 0 + 199.2647059 20.44117647x + x2 = 0 + 199.2647059 Combine like terms: 0 + 199.2647059 = 199.2647059 20.44117647x + x2 = 199.2647059 The x term is 20.44117647x. Take half its coefficient (10.22058824). Square it (104.4604240) and add it to both sides. Add '104.4604240' to each side of the equation. 20.44117647x + 104.4604240 + x2 = 199.2647059 + 104.4604240 Reorder the terms: 104.4604240 + 20.44117647x + x2 = 199.2647059 + 104.4604240 Combine like terms: 199.2647059 + 104.4604240 = 303.7251299 104.4604240 + 20.44117647x + x2 = 303.7251299 Factor a perfect square on the left side: (x + 10.22058824)(x + 10.22058824) = 303.7251299 Calculate the square root of the right side: 17.427711551 Break this problem into two subproblems by setting (x + 10.22058824) equal to 17.427711551 and -17.427711551.Subproblem 1
x + 10.22058824 = 17.427711551 Simplifying x + 10.22058824 = 17.427711551 Reorder the terms: 10.22058824 + x = 17.427711551 Solving 10.22058824 + x = 17.427711551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.22058824' to each side of the equation. 10.22058824 + -10.22058824 + x = 17.427711551 + -10.22058824 Combine like terms: 10.22058824 + -10.22058824 = 0.00000000 0.00000000 + x = 17.427711551 + -10.22058824 x = 17.427711551 + -10.22058824 Combine like terms: 17.427711551 + -10.22058824 = 7.207123311 x = 7.207123311 Simplifying x = 7.207123311Subproblem 2
x + 10.22058824 = -17.427711551 Simplifying x + 10.22058824 = -17.427711551 Reorder the terms: 10.22058824 + x = -17.427711551 Solving 10.22058824 + x = -17.427711551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.22058824' to each side of the equation. 10.22058824 + -10.22058824 + x = -17.427711551 + -10.22058824 Combine like terms: 10.22058824 + -10.22058824 = 0.00000000 0.00000000 + x = -17.427711551 + -10.22058824 x = -17.427711551 + -10.22058824 Combine like terms: -17.427711551 + -10.22058824 = -27.648299791 x = -27.648299791 Simplifying x = -27.648299791Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.207123311, -27.648299791}
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