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Simplifying (365x) + -1(0.1x2) = 20000 Remove parenthesis around (0.1x2) (365x) + -1 * 0.1x2 = 20000 Multiply -1 * 0.1 (365x) + -0.1x2 = 20000 Solving (365x) + -0.1x2 = 20000 Solving for variable 'x'. Reorder the terms: -20000 + (365x) + -0.1x2 = 20000 + -20000 Combine like terms: 20000 + -20000 = 0 -20000 + (365x) + -0.1x2 = 0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 200000 + (-3650x) + x2 = 0 Move the constant term to the right: Add '-200000' to each side of the equation. 200000 + (-3650x) + -200000 + x2 = 0 + -200000 Reorder the terms: 200000 + -200000 + (-3650x) + x2 = 0 + -200000 Combine like terms: 200000 + -200000 = 0 0 + (-3650x) + x2 = 0 + -200000 (-3650x) + x2 = 0 + -200000 Combine like terms: 0 + -200000 = -200000 (-3650x) + x2 = -200000 The x term is (-3650x). Take half its coefficient (-1825). Square it (3330625) and add it to both sides. Add '3330625' to each side of the equation. (-3650x) + 3330625 + x2 = -200000 + 3330625 Reorder the terms: 3330625 + (-3650x) + x2 = -200000 + 3330625 Combine like terms: -200000 + 3330625 = 3130625 3330625 + (-3650x) + x2 = 3130625 Factor a perfect square on the left side: (x + -1825)(x + -1825) = 3130625 Calculate the square root of the right side: 1769.357227922 Break this problem into two subproblems by setting (x + -1825) equal to 1769.357227922 and -1769.357227922.Subproblem 1
x + -1825 = 1769.357227922 Simplifying x + -1825 = 1769.357227922 Reorder the terms: -1825 + x = 1769.357227922 Solving -1825 + x = 1769.357227922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1825' to each side of the equation. -1825 + 1825 + x = 1769.357227922 + 1825 Combine like terms: -1825 + 1825 = 0 0 + x = 1769.357227922 + 1825 x = 1769.357227922 + 1825 Combine like terms: 1769.357227922 + 1825 = 3594.357227922 x = 3594.357227922 Simplifying x = 3594.357227922Subproblem 2
x + -1825 = -1769.357227922 Simplifying x + -1825 = -1769.357227922 Reorder the terms: -1825 + x = -1769.357227922 Solving -1825 + x = -1769.357227922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1825' to each side of the equation. -1825 + 1825 + x = -1769.357227922 + 1825 Combine like terms: -1825 + 1825 = 0 0 + x = -1769.357227922 + 1825 x = -1769.357227922 + 1825 Combine like terms: -1769.357227922 + 1825 = 55.642772078 x = 55.642772078 Simplifying x = 55.642772078Solution
The solution to the problem is based on the solutions from the subproblems. x = {3594.357227922, 55.642772078}
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