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Simplifying 64x = 81 + -1x2 Solving 64x = 81 + -1x2 Solving for variable 'x'. Reorder the terms: -81 + 64x + x2 = 81 + -1x2 + -81 + x2 Reorder the terms: -81 + 64x + x2 = 81 + -81 + -1x2 + x2 Combine like terms: 81 + -81 = 0 -81 + 64x + x2 = 0 + -1x2 + x2 -81 + 64x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -81 + 64x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + 64x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + 64x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 64x + x2 = 0 + 81 64x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 64x + x2 = 81 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 = 81 + 1024 Reorder the terms: 1024 + 64x + x2 = 81 + 1024 Combine like terms: 81 + 1024 = 1105 1024 + 64x + x2 = 1105 Factor a perfect square on the left side: (x + 32)(x + 32) = 1105 Calculate the square root of the right side: 33.241540277 Break this problem into two subproblems by setting (x + 32) equal to 33.241540277 and -33.241540277.Subproblem 1
x + 32 = 33.241540277 Simplifying x + 32 = 33.241540277 Reorder the terms: 32 + x = 33.241540277 Solving 32 + x = 33.241540277 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 = 33.241540277 + -32 Combine like terms: 32 + -32 = 0 0 + x = 33.241540277 + -32 x = 33.241540277 + -32 Combine like terms: 33.241540277 + -32 = 1.241540277 x = 1.241540277 Simplifying x = 1.241540277Subproblem 2
x + 32 = -33.241540277 Simplifying x + 32 = -33.241540277 Reorder the terms: 32 + x = -33.241540277 Solving 32 + x = -33.241540277 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 = -33.241540277 + -32 Combine like terms: 32 + -32 = 0 0 + x = -33.241540277 + -32 x = -33.241540277 + -32 Combine like terms: -33.241540277 + -32 = -65.241540277 x = -65.241540277 Simplifying x = -65.241540277Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.241540277, -65.241540277}
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