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Simplifying x2 + 40x + 156 = 0 Reorder the terms: 156 + 40x + x2 = 0 Solving 156 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-156' to each side of the equation. 156 + 40x + -156 + x2 = 0 + -156 Reorder the terms: 156 + -156 + 40x + x2 = 0 + -156 Combine like terms: 156 + -156 = 0 0 + 40x + x2 = 0 + -156 40x + x2 = 0 + -156 Combine like terms: 0 + -156 = -156 40x + x2 = -156 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 = -156 + 400 Reorder the terms: 400 + 40x + x2 = -156 + 400 Combine like terms: -156 + 400 = 244 400 + 40x + x2 = 244 Factor a perfect square on the left side: (x + 20)(x + 20) = 244 Calculate the square root of the right side: 15.620499352 Break this problem into two subproblems by setting (x + 20) equal to 15.620499352 and -15.620499352.Subproblem 1
x + 20 = 15.620499352 Simplifying x + 20 = 15.620499352 Reorder the terms: 20 + x = 15.620499352 Solving 20 + x = 15.620499352 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 = 15.620499352 + -20 Combine like terms: 20 + -20 = 0 0 + x = 15.620499352 + -20 x = 15.620499352 + -20 Combine like terms: 15.620499352 + -20 = -4.379500648 x = -4.379500648 Simplifying x = -4.379500648Subproblem 2
x + 20 = -15.620499352 Simplifying x + 20 = -15.620499352 Reorder the terms: 20 + x = -15.620499352 Solving 20 + x = -15.620499352 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 = -15.620499352 + -20 Combine like terms: 20 + -20 = 0 0 + x = -15.620499352 + -20 x = -15.620499352 + -20 Combine like terms: -15.620499352 + -20 = -35.620499352 x = -35.620499352 Simplifying x = -35.620499352Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.379500648, -35.620499352}
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