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Simplifying X2 + -16X + -936 = 0 Reorder the terms: -936 + -16X + X2 = 0 Solving -936 + -16X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '936' to each side of the equation. -936 + -16X + 936 + X2 = 0 + 936 Reorder the terms: -936 + 936 + -16X + X2 = 0 + 936 Combine like terms: -936 + 936 = 0 0 + -16X + X2 = 0 + 936 -16X + X2 = 0 + 936 Combine like terms: 0 + 936 = 936 -16X + X2 = 936 The X term is -16X. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16X + 64 + X2 = 936 + 64 Reorder the terms: 64 + -16X + X2 = 936 + 64 Combine like terms: 936 + 64 = 1000 64 + -16X + X2 = 1000 Factor a perfect square on the left side: (X + -8)(X + -8) = 1000 Calculate the square root of the right side: 31.622776602 Break this problem into two subproblems by setting (X + -8) equal to 31.622776602 and -31.622776602.Subproblem 1
X + -8 = 31.622776602 Simplifying X + -8 = 31.622776602 Reorder the terms: -8 + X = 31.622776602 Solving -8 + X = 31.622776602 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + X = 31.622776602 + 8 Combine like terms: -8 + 8 = 0 0 + X = 31.622776602 + 8 X = 31.622776602 + 8 Combine like terms: 31.622776602 + 8 = 39.622776602 X = 39.622776602 Simplifying X = 39.622776602Subproblem 2
X + -8 = -31.622776602 Simplifying X + -8 = -31.622776602 Reorder the terms: -8 + X = -31.622776602 Solving -8 + X = -31.622776602 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + X = -31.622776602 + 8 Combine like terms: -8 + 8 = 0 0 + X = -31.622776602 + 8 X = -31.622776602 + 8 Combine like terms: -31.622776602 + 8 = -23.622776602 X = -23.622776602 Simplifying X = -23.622776602Solution
The solution to the problem is based on the solutions from the subproblems. X = {39.622776602, -23.622776602}
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