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Simplifying X2 + 8X = 64 Reorder the terms: 8X + X2 = 64 Solving 8X + X2 = 64 Solving for variable 'X'. Reorder the terms: -64 + 8X + X2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + 8X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 8X + 64 + X2 = 0 + 64 Reorder the terms: -64 + 64 + 8X + X2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 8X + X2 = 0 + 64 8X + X2 = 0 + 64 Combine like terms: 0 + 64 = 64 8X + X2 = 64 The X term is 8X. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8X + 16 + X2 = 64 + 16 Reorder the terms: 16 + 8X + X2 = 64 + 16 Combine like terms: 64 + 16 = 80 16 + 8X + X2 = 80 Factor a perfect square on the left side: (X + 4)(X + 4) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (X + 4) equal to 8.94427191 and -8.94427191.Subproblem 1
X + 4 = 8.94427191 Simplifying X + 4 = 8.94427191 Reorder the terms: 4 + X = 8.94427191 Solving 4 + X = 8.94427191 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + X = 8.94427191 + -4 Combine like terms: 4 + -4 = 0 0 + X = 8.94427191 + -4 X = 8.94427191 + -4 Combine like terms: 8.94427191 + -4 = 4.94427191 X = 4.94427191 Simplifying X = 4.94427191Subproblem 2
X + 4 = -8.94427191 Simplifying X + 4 = -8.94427191 Reorder the terms: 4 + X = -8.94427191 Solving 4 + X = -8.94427191 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + X = -8.94427191 + -4 Combine like terms: 4 + -4 = 0 0 + X = -8.94427191 + -4 X = -8.94427191 + -4 Combine like terms: -8.94427191 + -4 = -12.94427191 X = -12.94427191 Simplifying X = -12.94427191Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.94427191, -12.94427191}
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