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Simplifying x2 + 40x + -140 = 0 Reorder the terms: -140 + 40x + x2 = 0 Solving -140 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + 40x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 40x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 40x + x2 = 0 + 140 40x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 40x + x2 = 140 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 = 140 + 400 Reorder the terms: 400 + 40x + x2 = 140 + 400 Combine like terms: 140 + 400 = 540 400 + 40x + x2 = 540 Factor a perfect square on the left side: (x + 20)(x + 20) = 540 Calculate the square root of the right side: 23.237900077 Break this problem into two subproblems by setting (x + 20) equal to 23.237900077 and -23.237900077.Subproblem 1
x + 20 = 23.237900077 Simplifying x + 20 = 23.237900077 Reorder the terms: 20 + x = 23.237900077 Solving 20 + x = 23.237900077 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 = 23.237900077 + -20 Combine like terms: 20 + -20 = 0 0 + x = 23.237900077 + -20 x = 23.237900077 + -20 Combine like terms: 23.237900077 + -20 = 3.237900077 x = 3.237900077 Simplifying x = 3.237900077Subproblem 2
x + 20 = -23.237900077 Simplifying x + 20 = -23.237900077 Reorder the terms: 20 + x = -23.237900077 Solving 20 + x = -23.237900077 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 = -23.237900077 + -20 Combine like terms: 20 + -20 = 0 0 + x = -23.237900077 + -20 x = -23.237900077 + -20 Combine like terms: -23.237900077 + -20 = -43.237900077 x = -43.237900077 Simplifying x = -43.237900077Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.237900077, -43.237900077}
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