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Simplifying 0 = x2 + 40x + -8640000 Reorder the terms: 0 = -8640000 + 40x + x2 Solving 0 = -8640000 + 40x + x2 Solving for variable 'x'. Combine like terms: 0 + 8640000 = 8640000 8640000 + -40x + -1x2 = -8640000 + 40x + x2 + 8640000 + -40x + -1x2 Reorder the terms: 8640000 + -40x + -1x2 = -8640000 + 8640000 + 40x + -40x + x2 + -1x2 Combine like terms: -8640000 + 8640000 = 0 8640000 + -40x + -1x2 = 0 + 40x + -40x + x2 + -1x2 8640000 + -40x + -1x2 = 40x + -40x + x2 + -1x2 Combine like terms: 40x + -40x = 0 8640000 + -40x + -1x2 = 0 + x2 + -1x2 8640000 + -40x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 8640000 + -40x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8640000 + 40x + x2 = 0 Move the constant term to the right: Add '8640000' to each side of the equation. -8640000 + 40x + 8640000 + x2 = 0 + 8640000 Reorder the terms: -8640000 + 8640000 + 40x + x2 = 0 + 8640000 Combine like terms: -8640000 + 8640000 = 0 0 + 40x + x2 = 0 + 8640000 40x + x2 = 0 + 8640000 Combine like terms: 0 + 8640000 = 8640000 40x + x2 = 8640000 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 8640000 + 400 Reorder the terms: 400 + 40x + x2 = 8640000 + 400 Combine like terms: 8640000 + 400 = 8640400 400 + 40x + x2 = 8640400 Factor a perfect square on the left side: (x + 20)(x + 20) = 8640400 Calculate the square root of the right side: 2939.455731934 Break this problem into two subproblems by setting (x + 20) equal to 2939.455731934 and -2939.455731934.Subproblem 1
x + 20 = 2939.455731934 Simplifying x + 20 = 2939.455731934 Reorder the terms: 20 + x = 2939.455731934 Solving 20 + x = 2939.455731934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 2939.455731934 + -20 Combine like terms: 20 + -20 = 0 0 + x = 2939.455731934 + -20 x = 2939.455731934 + -20 Combine like terms: 2939.455731934 + -20 = 2919.455731934 x = 2919.455731934 Simplifying x = 2919.455731934Subproblem 2
x + 20 = -2939.455731934 Simplifying x + 20 = -2939.455731934 Reorder the terms: 20 + x = -2939.455731934 Solving 20 + x = -2939.455731934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -2939.455731934 + -20 Combine like terms: 20 + -20 = 0 0 + x = -2939.455731934 + -20 x = -2939.455731934 + -20 Combine like terms: -2939.455731934 + -20 = -2959.455731934 x = -2959.455731934 Simplifying x = -2959.455731934Solution
The solution to the problem is based on the solutions from the subproblems. x = {2919.455731934, -2959.455731934}
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