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Simplifying 575 = 1.36x2 + 27.8x Reorder the terms: 575 = 27.8x + 1.36x2 Solving 575 = 27.8x + 1.36x2 Solving for variable 'x'. Reorder the terms: 575 + -27.8x + -1.36x2 = 27.8x + -27.8x + 1.36x2 + -1.36x2 Combine like terms: 27.8x + -27.8x = 0.0 575 + -27.8x + -1.36x2 = 0.0 + 1.36x2 + -1.36x2 575 + -27.8x + -1.36x2 = 1.36x2 + -1.36x2 Combine like terms: 1.36x2 + -1.36x2 = 0.00 575 + -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'. -422.7941176 + 20.44117647x + x2 = 0 Move the constant term to the right: Add '422.7941176' to each side of the equation. -422.7941176 + 20.44117647x + 422.7941176 + x2 = 0 + 422.7941176 Reorder the terms: -422.7941176 + 422.7941176 + 20.44117647x + x2 = 0 + 422.7941176 Combine like terms: -422.7941176 + 422.7941176 = 0.0000000 0.0000000 + 20.44117647x + x2 = 0 + 422.7941176 20.44117647x + x2 = 0 + 422.7941176 Combine like terms: 0 + 422.7941176 = 422.7941176 20.44117647x + x2 = 422.7941176 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 = 422.7941176 + 104.4604240 Reorder the terms: 104.4604240 + 20.44117647x + x2 = 422.7941176 + 104.4604240 Combine like terms: 422.7941176 + 104.4604240 = 527.2545416 104.4604240 + 20.44117647x + x2 = 527.2545416 Factor a perfect square on the left side: (x + 10.22058824)(x + 10.22058824) = 527.2545416 Calculate the square root of the right side: 22.9620239 Break this problem into two subproblems by setting (x + 10.22058824) equal to 22.9620239 and -22.9620239.Subproblem 1
x + 10.22058824 = 22.9620239 Simplifying x + 10.22058824 = 22.9620239 Reorder the terms: 10.22058824 + x = 22.9620239 Solving 10.22058824 + x = 22.9620239 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 = 22.9620239 + -10.22058824 Combine like terms: 10.22058824 + -10.22058824 = 0.00000000 0.00000000 + x = 22.9620239 + -10.22058824 x = 22.9620239 + -10.22058824 Combine like terms: 22.9620239 + -10.22058824 = 12.74143566 x = 12.74143566 Simplifying x = 12.74143566Subproblem 2
x + 10.22058824 = -22.9620239 Simplifying x + 10.22058824 = -22.9620239 Reorder the terms: 10.22058824 + x = -22.9620239 Solving 10.22058824 + x = -22.9620239 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 = -22.9620239 + -10.22058824 Combine like terms: 10.22058824 + -10.22058824 = 0.00000000 0.00000000 + x = -22.9620239 + -10.22058824 x = -22.9620239 + -10.22058824 Combine like terms: -22.9620239 + -10.22058824 = -33.18261214 x = -33.18261214 Simplifying x = -33.18261214Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.74143566, -33.18261214}
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