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Simplifying x2 + 156x + 355 = 0 Reorder the terms: 355 + 156x + x2 = 0 Solving 355 + 156x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-355' to each side of the equation. 355 + 156x + -355 + x2 = 0 + -355 Reorder the terms: 355 + -355 + 156x + x2 = 0 + -355 Combine like terms: 355 + -355 = 0 0 + 156x + x2 = 0 + -355 156x + x2 = 0 + -355 Combine like terms: 0 + -355 = -355 156x + x2 = -355 The x term is 156x. Take half its coefficient (78). Square it (6084) and add it to both sides. Add '6084' to each side of the equation. 156x + 6084 + x2 = -355 + 6084 Reorder the terms: 6084 + 156x + x2 = -355 + 6084 Combine like terms: -355 + 6084 = 5729 6084 + 156x + x2 = 5729 Factor a perfect square on the left side: (x + 78)(x + 78) = 5729 Calculate the square root of the right side: 75.690157881 Break this problem into two subproblems by setting (x + 78) equal to 75.690157881 and -75.690157881.Subproblem 1
x + 78 = 75.690157881 Simplifying x + 78 = 75.690157881 Reorder the terms: 78 + x = 75.690157881 Solving 78 + x = 75.690157881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-78' to each side of the equation. 78 + -78 + x = 75.690157881 + -78 Combine like terms: 78 + -78 = 0 0 + x = 75.690157881 + -78 x = 75.690157881 + -78 Combine like terms: 75.690157881 + -78 = -2.309842119 x = -2.309842119 Simplifying x = -2.309842119Subproblem 2
x + 78 = -75.690157881 Simplifying x + 78 = -75.690157881 Reorder the terms: 78 + x = -75.690157881 Solving 78 + x = -75.690157881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-78' to each side of the equation. 78 + -78 + x = -75.690157881 + -78 Combine like terms: 78 + -78 = 0 0 + x = -75.690157881 + -78 x = -75.690157881 + -78 Combine like terms: -75.690157881 + -78 = -153.690157881 x = -153.690157881 Simplifying x = -153.690157881Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.309842119, -153.690157881}
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