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Simplifying x2 + 60x + 792 = 0 Reorder the terms: 792 + 60x + x2 = 0 Solving 792 + 60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-792' to each side of the equation. 792 + 60x + -792 + x2 = 0 + -792 Reorder the terms: 792 + -792 + 60x + x2 = 0 + -792 Combine like terms: 792 + -792 = 0 0 + 60x + x2 = 0 + -792 60x + x2 = 0 + -792 Combine like terms: 0 + -792 = -792 60x + x2 = -792 The x term is 60x. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60x + 900 + x2 = -792 + 900 Reorder the terms: 900 + 60x + x2 = -792 + 900 Combine like terms: -792 + 900 = 108 900 + 60x + x2 = 108 Factor a perfect square on the left side: (x + 30)(x + 30) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (x + 30) equal to 10.392304845 and -10.392304845.Subproblem 1
x + 30 = 10.392304845 Simplifying x + 30 = 10.392304845 Reorder the terms: 30 + x = 10.392304845 Solving 30 + x = 10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 10.392304845 + -30 Combine like terms: 30 + -30 = 0 0 + x = 10.392304845 + -30 x = 10.392304845 + -30 Combine like terms: 10.392304845 + -30 = -19.607695155 x = -19.607695155 Simplifying x = -19.607695155Subproblem 2
x + 30 = -10.392304845 Simplifying x + 30 = -10.392304845 Reorder the terms: 30 + x = -10.392304845 Solving 30 + x = -10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -10.392304845 + -30 Combine like terms: 30 + -30 = 0 0 + x = -10.392304845 + -30 x = -10.392304845 + -30 Combine like terms: -10.392304845 + -30 = -40.392304845 x = -40.392304845 Simplifying x = -40.392304845Solution
The solution to the problem is based on the solutions from the subproblems. x = {-19.607695155, -40.392304845}
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