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Simplifying x2 + 40x + -600 = 0 Reorder the terms: -600 + 40x + x2 = 0 Solving -600 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '600' to each side of the equation. -600 + 40x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + 40x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + 40x + x2 = 0 + 600 40x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 40x + x2 = 600 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 = 600 + 400 Reorder the terms: 400 + 40x + x2 = 600 + 400 Combine like terms: 600 + 400 = 1000 400 + 40x + x2 = 1000 Factor a perfect square on the left side: (x + 20)(x + 20) = 1000 Calculate the square root of the right side: 31.622776602 Break this problem into two subproblems by setting (x + 20) equal to 31.622776602 and -31.622776602.Subproblem 1
x + 20 = 31.622776602 Simplifying x + 20 = 31.622776602 Reorder the terms: 20 + x = 31.622776602 Solving 20 + x = 31.622776602 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 = 31.622776602 + -20 Combine like terms: 20 + -20 = 0 0 + x = 31.622776602 + -20 x = 31.622776602 + -20 Combine like terms: 31.622776602 + -20 = 11.622776602 x = 11.622776602 Simplifying x = 11.622776602Subproblem 2
x + 20 = -31.622776602 Simplifying x + 20 = -31.622776602 Reorder the terms: 20 + x = -31.622776602 Solving 20 + x = -31.622776602 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 = -31.622776602 + -20 Combine like terms: 20 + -20 = 0 0 + x = -31.622776602 + -20 x = -31.622776602 + -20 Combine like terms: -31.622776602 + -20 = -51.622776602 x = -51.622776602 Simplifying x = -51.622776602Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.622776602, -51.622776602}
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