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Simplifying 5000000 = 1.36x2 + 27.8x + 304 Reorder the terms: 5000000 = 304 + 27.8x + 1.36x2 Solving 5000000 = 304 + 27.8x + 1.36x2 Solving for variable 'x'. Combine like terms: 5000000 + -304 = 4999696 4999696 + -27.8x + -1.36x2 = 304 + 27.8x + 1.36x2 + -304 + -27.8x + -1.36x2 Reorder the terms: 4999696 + -27.8x + -1.36x2 = 304 + -304 + 27.8x + -27.8x + 1.36x2 + -1.36x2 Combine like terms: 304 + -304 = 0 4999696 + -27.8x + -1.36x2 = 0 + 27.8x + -27.8x + 1.36x2 + -1.36x2 4999696 + -27.8x + -1.36x2 = 27.8x + -27.8x + 1.36x2 + -1.36x2 Combine like terms: 27.8x + -27.8x = 0.0 4999696 + -27.8x + -1.36x2 = 0.0 + 1.36x2 + -1.36x2 4999696 + -27.8x + -1.36x2 = 1.36x2 + -1.36x2 Combine like terms: 1.36x2 + -1.36x2 = 0.00 4999696 + -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'. -3676247.059 + 20.44117647x + x2 = 0 Move the constant term to the right: Add '3676247.059' to each side of the equation. -3676247.059 + 20.44117647x + 3676247.059 + x2 = 0 + 3676247.059 Reorder the terms: -3676247.059 + 3676247.059 + 20.44117647x + x2 = 0 + 3676247.059 Combine like terms: -3676247.059 + 3676247.059 = 0.000 0.000 + 20.44117647x + x2 = 0 + 3676247.059 20.44117647x + x2 = 0 + 3676247.059 Combine like terms: 0 + 3676247.059 = 3676247.059 20.44117647x + x2 = 3676247.059 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 = 3676247.059 + 104.4604240 Reorder the terms: 104.4604240 + 20.44117647x + x2 = 3676247.059 + 104.4604240 Combine like terms: 3676247.059 + 104.4604240 = 3676351.519424 104.4604240 + 20.44117647x + x2 = 3676351.519424 Factor a perfect square on the left side: (x + 10.22058824)(x + 10.22058824) = 3676351.519424 Calculate the square root of the right side: 1917.38142252 Break this problem into two subproblems by setting (x + 10.22058824) equal to 1917.38142252 and -1917.38142252.Subproblem 1
x + 10.22058824 = 1917.38142252 Simplifying x + 10.22058824 = 1917.38142252 Reorder the terms: 10.22058824 + x = 1917.38142252 Solving 10.22058824 + x = 1917.38142252 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 = 1917.38142252 + -10.22058824 Combine like terms: 10.22058824 + -10.22058824 = 0.00000000 0.00000000 + x = 1917.38142252 + -10.22058824 x = 1917.38142252 + -10.22058824 Combine like terms: 1917.38142252 + -10.22058824 = 1907.16083428 x = 1907.16083428 Simplifying x = 1907.16083428Subproblem 2
x + 10.22058824 = -1917.38142252 Simplifying x + 10.22058824 = -1917.38142252 Reorder the terms: 10.22058824 + x = -1917.38142252 Solving 10.22058824 + x = -1917.38142252 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 = -1917.38142252 + -10.22058824 Combine like terms: 10.22058824 + -10.22058824 = 0.00000000 0.00000000 + x = -1917.38142252 + -10.22058824 x = -1917.38142252 + -10.22058824 Combine like terms: -1917.38142252 + -10.22058824 = -1927.60201076 x = -1927.60201076 Simplifying x = -1927.60201076Solution
The solution to the problem is based on the solutions from the subproblems. x = {1907.16083428, -1927.60201076}
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