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Simplifying 500000000 = 1.36(x * x) + 27.8x + 304 Multiply x * x 500000000 = 1.36(x2) + 27.8x + 304 Reorder the terms: 500000000 = 304 + 27.8x + 1.36x2 Solving 500000000 = 304 + 27.8x + 1.36x2 Solving for variable 'x'. Combine like terms: 500000000 + -304 = 499999696 499999696 + -27.8x + -1.36x2 = 304 + 27.8x + 1.36x2 + -304 + -27.8x + -1.36x2 Reorder the terms: 499999696 + -27.8x + -1.36x2 = 304 + -304 + 27.8x + -27.8x + 1.36x2 + -1.36x2 Combine like terms: 304 + -304 = 0 499999696 + -27.8x + -1.36x2 = 0 + 27.8x + -27.8x + 1.36x2 + -1.36x2 499999696 + -27.8x + -1.36x2 = 27.8x + -27.8x + 1.36x2 + -1.36x2 Combine like terms: 27.8x + -27.8x = 0.0 499999696 + -27.8x + -1.36x2 = 0.0 + 1.36x2 + -1.36x2 499999696 + -27.8x + -1.36x2 = 1.36x2 + -1.36x2 Combine like terms: 1.36x2 + -1.36x2 = 0.00 499999696 + -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'. -367646835.3 + 20.44117647x + x2 = 0 Move the constant term to the right: Add '367646835.3' to each side of the equation. -367646835.3 + 20.44117647x + 367646835.3 + x2 = 0 + 367646835.3 Reorder the terms: -367646835.3 + 367646835.3 + 20.44117647x + x2 = 0 + 367646835.3 Combine like terms: -367646835.3 + 367646835.3 = 0.0 0.0 + 20.44117647x + x2 = 0 + 367646835.3 20.44117647x + x2 = 0 + 367646835.3 Combine like terms: 0 + 367646835.3 = 367646835.3 20.44117647x + x2 = 367646835.3 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 = 367646835.3 + 104.4604240 Reorder the terms: 104.4604240 + 20.44117647x + x2 = 367646835.3 + 104.4604240 Combine like terms: 367646835.3 + 104.4604240 = 367646939.760424 104.4604240 + 20.44117647x + x2 = 367646939.760424 Factor a perfect square on the left side: (x + 10.22058824)(x + 10.22058824) = 367646939.760424 Calculate the square root of the right side: 19174.121616398 Break this problem into two subproblems by setting (x + 10.22058824) equal to 19174.121616398 and -19174.121616398.Subproblem 1
x + 10.22058824 = 19174.121616398 Simplifying x + 10.22058824 = 19174.121616398 Reorder the terms: 10.22058824 + x = 19174.121616398 Solving 10.22058824 + x = 19174.121616398 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 = 19174.121616398 + -10.22058824 Combine like terms: 10.22058824 + -10.22058824 = 0.00000000 0.00000000 + x = 19174.121616398 + -10.22058824 x = 19174.121616398 + -10.22058824 Combine like terms: 19174.121616398 + -10.22058824 = 19163.901028158 x = 19163.901028158 Simplifying x = 19163.901028158Subproblem 2
x + 10.22058824 = -19174.121616398 Simplifying x + 10.22058824 = -19174.121616398 Reorder the terms: 10.22058824 + x = -19174.121616398 Solving 10.22058824 + x = -19174.121616398 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 = -19174.121616398 + -10.22058824 Combine like terms: 10.22058824 + -10.22058824 = 0.00000000 0.00000000 + x = -19174.121616398 + -10.22058824 x = -19174.121616398 + -10.22058824 Combine like terms: -19174.121616398 + -10.22058824 = -19184.342204638 x = -19184.342204638 Simplifying x = -19184.342204638Solution
The solution to the problem is based on the solutions from the subproblems. x = {19163.901028158, -19184.342204638}
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