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Simplifying x(x + 64) = 126 Reorder the terms: x(64 + x) = 126 (64 * x + x * x) = 126 (64x + x2) = 126 Solving 64x + x2 = 126 Solving for variable 'x'. Reorder the terms: -126 + 64x + x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -126 + 64x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '126' to each side of the equation. -126 + 64x + 126 + x2 = 0 + 126 Reorder the terms: -126 + 126 + 64x + x2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + 64x + x2 = 0 + 126 64x + x2 = 0 + 126 Combine like terms: 0 + 126 = 126 64x + x2 = 126 The x term is 64x. Take half its coefficient (32). Square it (1024) and add it to both sides. Add '1024' to each side of the equation. 64x + 1024 + x2 = 126 + 1024 Reorder the terms: 1024 + 64x + x2 = 126 + 1024 Combine like terms: 126 + 1024 = 1150 1024 + 64x + x2 = 1150 Factor a perfect square on the left side: (x + 32)(x + 32) = 1150 Calculate the square root of the right side: 33.911649916 Break this problem into two subproblems by setting (x + 32) equal to 33.911649916 and -33.911649916.Subproblem 1
x + 32 = 33.911649916 Simplifying x + 32 = 33.911649916 Reorder the terms: 32 + x = 33.911649916 Solving 32 + x = 33.911649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x = 33.911649916 + -32 Combine like terms: 32 + -32 = 0 0 + x = 33.911649916 + -32 x = 33.911649916 + -32 Combine like terms: 33.911649916 + -32 = 1.911649916 x = 1.911649916 Simplifying x = 1.911649916Subproblem 2
x + 32 = -33.911649916 Simplifying x + 32 = -33.911649916 Reorder the terms: 32 + x = -33.911649916 Solving 32 + x = -33.911649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x = -33.911649916 + -32 Combine like terms: 32 + -32 = 0 0 + x = -33.911649916 + -32 x = -33.911649916 + -32 Combine like terms: -33.911649916 + -32 = -65.911649916 x = -65.911649916 Simplifying x = -65.911649916Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.911649916, -65.911649916}
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