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Simplifying x2 + 40x + -2700 = 0 Reorder the terms: -2700 + 40x + x2 = 0 Solving -2700 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2700' to each side of the equation. -2700 + 40x + 2700 + x2 = 0 + 2700 Reorder the terms: -2700 + 2700 + 40x + x2 = 0 + 2700 Combine like terms: -2700 + 2700 = 0 0 + 40x + x2 = 0 + 2700 40x + x2 = 0 + 2700 Combine like terms: 0 + 2700 = 2700 40x + x2 = 2700 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 = 2700 + 400 Reorder the terms: 400 + 40x + x2 = 2700 + 400 Combine like terms: 2700 + 400 = 3100 400 + 40x + x2 = 3100 Factor a perfect square on the left side: (x + 20)(x + 20) = 3100 Calculate the square root of the right side: 55.677643628 Break this problem into two subproblems by setting (x + 20) equal to 55.677643628 and -55.677643628.Subproblem 1
x + 20 = 55.677643628 Simplifying x + 20 = 55.677643628 Reorder the terms: 20 + x = 55.677643628 Solving 20 + x = 55.677643628 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 = 55.677643628 + -20 Combine like terms: 20 + -20 = 0 0 + x = 55.677643628 + -20 x = 55.677643628 + -20 Combine like terms: 55.677643628 + -20 = 35.677643628 x = 35.677643628 Simplifying x = 35.677643628Subproblem 2
x + 20 = -55.677643628 Simplifying x + 20 = -55.677643628 Reorder the terms: 20 + x = -55.677643628 Solving 20 + x = -55.677643628 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 = -55.677643628 + -20 Combine like terms: 20 + -20 = 0 0 + x = -55.677643628 + -20 x = -55.677643628 + -20 Combine like terms: -55.677643628 + -20 = -75.677643628 x = -75.677643628 Simplifying x = -75.677643628Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.677643628, -75.677643628}
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