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Simplifying x2 + 32x + -480 = 0 Reorder the terms: -480 + 32x + x2 = 0 Solving -480 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '480' to each side of the equation. -480 + 32x + 480 + x2 = 0 + 480 Reorder the terms: -480 + 480 + 32x + x2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + 32x + x2 = 0 + 480 32x + x2 = 0 + 480 Combine like terms: 0 + 480 = 480 32x + x2 = 480 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = 480 + 256 Reorder the terms: 256 + 32x + x2 = 480 + 256 Combine like terms: 480 + 256 = 736 256 + 32x + x2 = 736 Factor a perfect square on the left side: (x + 16)(x + 16) = 736 Calculate the square root of the right side: 27.129319933 Break this problem into two subproblems by setting (x + 16) equal to 27.129319933 and -27.129319933.Subproblem 1
x + 16 = 27.129319933 Simplifying x + 16 = 27.129319933 Reorder the terms: 16 + x = 27.129319933 Solving 16 + x = 27.129319933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 27.129319933 + -16 Combine like terms: 16 + -16 = 0 0 + x = 27.129319933 + -16 x = 27.129319933 + -16 Combine like terms: 27.129319933 + -16 = 11.129319933 x = 11.129319933 Simplifying x = 11.129319933Subproblem 2
x + 16 = -27.129319933 Simplifying x + 16 = -27.129319933 Reorder the terms: 16 + x = -27.129319933 Solving 16 + x = -27.129319933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -27.129319933 + -16 Combine like terms: 16 + -16 = 0 0 + x = -27.129319933 + -16 x = -27.129319933 + -16 Combine like terms: -27.129319933 + -16 = -43.129319933 x = -43.129319933 Simplifying x = -43.129319933Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.129319933, -43.129319933}
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