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Simplifying 0 = 20000 + -220x + 0.045x2 Solving 0 = 20000 + -220x + 0.045x2 Solving for variable 'x'. Combine like terms: 0 + -20000 = -20000 -20000 + 220x + -0.045x2 = 20000 + -220x + 0.045x2 + -20000 + 220x + -0.045x2 Reorder the terms: -20000 + 220x + -0.045x2 = 20000 + -20000 + -220x + 220x + 0.045x2 + -0.045x2 Combine like terms: 20000 + -20000 = 0 -20000 + 220x + -0.045x2 = 0 + -220x + 220x + 0.045x2 + -0.045x2 -20000 + 220x + -0.045x2 = -220x + 220x + 0.045x2 + -0.045x2 Combine like terms: -220x + 220x = 0 -20000 + 220x + -0.045x2 = 0 + 0.045x2 + -0.045x2 -20000 + 220x + -0.045x2 = 0.045x2 + -0.045x2 Combine like terms: 0.045x2 + -0.045x2 = 0.000 -20000 + 220x + -0.045x2 = 0.000 Begin completing the square. Divide all terms by -0.045 the coefficient of the squared term: Divide each side by '-0.045'. 444444.4444 + -4888.888889x + x2 = 0 Move the constant term to the right: Add '-444444.4444' to each side of the equation. 444444.4444 + -4888.888889x + -444444.4444 + x2 = 0 + -444444.4444 Reorder the terms: 444444.4444 + -444444.4444 + -4888.888889x + x2 = 0 + -444444.4444 Combine like terms: 444444.4444 + -444444.4444 = 0.0000 0.0000 + -4888.888889x + x2 = 0 + -444444.4444 -4888.888889x + x2 = 0 + -444444.4444 Combine like terms: 0 + -444444.4444 = -444444.4444 -4888.888889x + x2 = -444444.4444 The x term is -4888.888889x. Take half its coefficient (-2444.444445). Square it (5975308.645) and add it to both sides. Add '5975308.645' to each side of the equation. -4888.888889x + 5975308.645 + x2 = -444444.4444 + 5975308.645 Reorder the terms: 5975308.645 + -4888.888889x + x2 = -444444.4444 + 5975308.645 Combine like terms: -444444.4444 + 5975308.645 = 5530864.2006 5975308.645 + -4888.888889x + x2 = 5530864.2006 Factor a perfect square on the left side: (x + -2444.444445)(x + -2444.444445) = 5530864.2006 Calculate the square root of the right side: 2351.778943821 Break this problem into two subproblems by setting (x + -2444.444445) equal to 2351.778943821 and -2351.778943821.Subproblem 1
x + -2444.444445 = 2351.778943821 Simplifying x + -2444.444445 = 2351.778943821 Reorder the terms: -2444.444445 + x = 2351.778943821 Solving -2444.444445 + x = 2351.778943821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2444.444445' to each side of the equation. -2444.444445 + 2444.444445 + x = 2351.778943821 + 2444.444445 Combine like terms: -2444.444445 + 2444.444445 = 0.000000 0.000000 + x = 2351.778943821 + 2444.444445 x = 2351.778943821 + 2444.444445 Combine like terms: 2351.778943821 + 2444.444445 = 4796.223388821 x = 4796.223388821 Simplifying x = 4796.223388821Subproblem 2
x + -2444.444445 = -2351.778943821 Simplifying x + -2444.444445 = -2351.778943821 Reorder the terms: -2444.444445 + x = -2351.778943821 Solving -2444.444445 + x = -2351.778943821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2444.444445' to each side of the equation. -2444.444445 + 2444.444445 + x = -2351.778943821 + 2444.444445 Combine like terms: -2444.444445 + 2444.444445 = 0.000000 0.000000 + x = -2351.778943821 + 2444.444445 x = -2351.778943821 + 2444.444445 Combine like terms: -2351.778943821 + 2444.444445 = 92.665501179 x = 92.665501179 Simplifying x = 92.665501179Solution
The solution to the problem is based on the solutions from the subproblems. x = {4796.223388821, 92.665501179}
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