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Simplifying x2 + 12x + -960 = 0 Reorder the terms: -960 + 12x + x2 = 0 Solving -960 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '960' to each side of the equation. -960 + 12x + 960 + x2 = 0 + 960 Reorder the terms: -960 + 960 + 12x + x2 = 0 + 960 Combine like terms: -960 + 960 = 0 0 + 12x + x2 = 0 + 960 12x + x2 = 0 + 960 Combine like terms: 0 + 960 = 960 12x + x2 = 960 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 960 + 36 Reorder the terms: 36 + 12x + x2 = 960 + 36 Combine like terms: 960 + 36 = 996 36 + 12x + x2 = 996 Factor a perfect square on the left side: (x + 6)(x + 6) = 996 Calculate the square root of the right side: 31.559467676 Break this problem into two subproblems by setting (x + 6) equal to 31.559467676 and -31.559467676.Subproblem 1
x + 6 = 31.559467676 Simplifying x + 6 = 31.559467676 Reorder the terms: 6 + x = 31.559467676 Solving 6 + x = 31.559467676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 31.559467676 + -6 Combine like terms: 6 + -6 = 0 0 + x = 31.559467676 + -6 x = 31.559467676 + -6 Combine like terms: 31.559467676 + -6 = 25.559467676 x = 25.559467676 Simplifying x = 25.559467676Subproblem 2
x + 6 = -31.559467676 Simplifying x + 6 = -31.559467676 Reorder the terms: 6 + x = -31.559467676 Solving 6 + x = -31.559467676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -31.559467676 + -6 Combine like terms: 6 + -6 = 0 0 + x = -31.559467676 + -6 x = -31.559467676 + -6 Combine like terms: -31.559467676 + -6 = -37.559467676 x = -37.559467676 Simplifying x = -37.559467676Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.559467676, -37.559467676}
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