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Simplifying -800 + 40.4x + -0.02x2 = 0 Solving -800 + 40.4x + -0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. 40000 + -2020x + x2 = 0 Move the constant term to the right: Add '-40000' to each side of the equation. 40000 + -2020x + -40000 + x2 = 0 + -40000 Reorder the terms: 40000 + -40000 + -2020x + x2 = 0 + -40000 Combine like terms: 40000 + -40000 = 0 0 + -2020x + x2 = 0 + -40000 -2020x + x2 = 0 + -40000 Combine like terms: 0 + -40000 = -40000 -2020x + x2 = -40000 The x term is -2020x. Take half its coefficient (-1010). Square it (1020100) and add it to both sides. Add '1020100' to each side of the equation. -2020x + 1020100 + x2 = -40000 + 1020100 Reorder the terms: 1020100 + -2020x + x2 = -40000 + 1020100 Combine like terms: -40000 + 1020100 = 980100 1020100 + -2020x + x2 = 980100 Factor a perfect square on the left side: (x + -1010)(x + -1010) = 980100 Calculate the square root of the right side: 990 Break this problem into two subproblems by setting (x + -1010) equal to 990 and -990.Subproblem 1
x + -1010 = 990 Simplifying x + -1010 = 990 Reorder the terms: -1010 + x = 990 Solving -1010 + x = 990 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1010' to each side of the equation. -1010 + 1010 + x = 990 + 1010 Combine like terms: -1010 + 1010 = 0 0 + x = 990 + 1010 x = 990 + 1010 Combine like terms: 990 + 1010 = 2000 x = 2000 Simplifying x = 2000Subproblem 2
x + -1010 = -990 Simplifying x + -1010 = -990 Reorder the terms: -1010 + x = -990 Solving -1010 + x = -990 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1010' to each side of the equation. -1010 + 1010 + x = -990 + 1010 Combine like terms: -1010 + 1010 = 0 0 + x = -990 + 1010 x = -990 + 1010 Combine like terms: -990 + 1010 = 20 x = 20 Simplifying x = 20Solution
The solution to the problem is based on the solutions from the subproblems. x = {2000, 20}
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