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Simplifying x2 + 40x + 77 = 0 Reorder the terms: 77 + 40x + x2 = 0 Solving 77 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-77' to each side of the equation. 77 + 40x + -77 + x2 = 0 + -77 Reorder the terms: 77 + -77 + 40x + x2 = 0 + -77 Combine like terms: 77 + -77 = 0 0 + 40x + x2 = 0 + -77 40x + x2 = 0 + -77 Combine like terms: 0 + -77 = -77 40x + x2 = -77 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 = -77 + 400 Reorder the terms: 400 + 40x + x2 = -77 + 400 Combine like terms: -77 + 400 = 323 400 + 40x + x2 = 323 Factor a perfect square on the left side: (x + 20)(x + 20) = 323 Calculate the square root of the right side: 17.972200756 Break this problem into two subproblems by setting (x + 20) equal to 17.972200756 and -17.972200756.Subproblem 1
x + 20 = 17.972200756 Simplifying x + 20 = 17.972200756 Reorder the terms: 20 + x = 17.972200756 Solving 20 + x = 17.972200756 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 = 17.972200756 + -20 Combine like terms: 20 + -20 = 0 0 + x = 17.972200756 + -20 x = 17.972200756 + -20 Combine like terms: 17.972200756 + -20 = -2.027799244 x = -2.027799244 Simplifying x = -2.027799244Subproblem 2
x + 20 = -17.972200756 Simplifying x + 20 = -17.972200756 Reorder the terms: 20 + x = -17.972200756 Solving 20 + x = -17.972200756 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 = -17.972200756 + -20 Combine like terms: 20 + -20 = 0 0 + x = -17.972200756 + -20 x = -17.972200756 + -20 Combine like terms: -17.972200756 + -20 = -37.972200756 x = -37.972200756 Simplifying x = -37.972200756Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.027799244, -37.972200756}
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