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Simplifying x2 + 156x + 1600 = 0 Reorder the terms: 1600 + 156x + x2 = 0 Solving 1600 + 156x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1600' to each side of the equation. 1600 + 156x + -1600 + x2 = 0 + -1600 Reorder the terms: 1600 + -1600 + 156x + x2 = 0 + -1600 Combine like terms: 1600 + -1600 = 0 0 + 156x + x2 = 0 + -1600 156x + x2 = 0 + -1600 Combine like terms: 0 + -1600 = -1600 156x + x2 = -1600 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 = -1600 + 6084 Reorder the terms: 6084 + 156x + x2 = -1600 + 6084 Combine like terms: -1600 + 6084 = 4484 6084 + 156x + x2 = 4484 Factor a perfect square on the left side: (x + 78)(x + 78) = 4484 Calculate the square root of the right side: 66.962676171 Break this problem into two subproblems by setting (x + 78) equal to 66.962676171 and -66.962676171.Subproblem 1
x + 78 = 66.962676171 Simplifying x + 78 = 66.962676171 Reorder the terms: 78 + x = 66.962676171 Solving 78 + x = 66.962676171 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 = 66.962676171 + -78 Combine like terms: 78 + -78 = 0 0 + x = 66.962676171 + -78 x = 66.962676171 + -78 Combine like terms: 66.962676171 + -78 = -11.037323829 x = -11.037323829 Simplifying x = -11.037323829Subproblem 2
x + 78 = -66.962676171 Simplifying x + 78 = -66.962676171 Reorder the terms: 78 + x = -66.962676171 Solving 78 + x = -66.962676171 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 = -66.962676171 + -78 Combine like terms: 78 + -78 = 0 0 + x = -66.962676171 + -78 x = -66.962676171 + -78 Combine like terms: -66.962676171 + -78 = -144.962676171 x = -144.962676171 Simplifying x = -144.962676171Solution
The solution to the problem is based on the solutions from the subproblems. x = {-11.037323829, -144.962676171}
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