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Simplifying x2 + 12x + -320 = 0 Reorder the terms: -320 + 12x + x2 = 0 Solving -320 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '320' to each side of the equation. -320 + 12x + 320 + x2 = 0 + 320 Reorder the terms: -320 + 320 + 12x + x2 = 0 + 320 Combine like terms: -320 + 320 = 0 0 + 12x + x2 = 0 + 320 12x + x2 = 0 + 320 Combine like terms: 0 + 320 = 320 12x + x2 = 320 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 = 320 + 36 Reorder the terms: 36 + 12x + x2 = 320 + 36 Combine like terms: 320 + 36 = 356 36 + 12x + x2 = 356 Factor a perfect square on the left side: (x + 6)(x + 6) = 356 Calculate the square root of the right side: 18.867962264 Break this problem into two subproblems by setting (x + 6) equal to 18.867962264 and -18.867962264.Subproblem 1
x + 6 = 18.867962264 Simplifying x + 6 = 18.867962264 Reorder the terms: 6 + x = 18.867962264 Solving 6 + x = 18.867962264 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 = 18.867962264 + -6 Combine like terms: 6 + -6 = 0 0 + x = 18.867962264 + -6 x = 18.867962264 + -6 Combine like terms: 18.867962264 + -6 = 12.867962264 x = 12.867962264 Simplifying x = 12.867962264Subproblem 2
x + 6 = -18.867962264 Simplifying x + 6 = -18.867962264 Reorder the terms: 6 + x = -18.867962264 Solving 6 + x = -18.867962264 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 = -18.867962264 + -6 Combine like terms: 6 + -6 = 0 0 + x = -18.867962264 + -6 x = -18.867962264 + -6 Combine like terms: -18.867962264 + -6 = -24.867962264 x = -24.867962264 Simplifying x = -24.867962264Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.867962264, -24.867962264}
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