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Simplifying x2 + -64x + 376 = 0 Reorder the terms: 376 + -64x + x2 = 0 Solving 376 + -64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-376' to each side of the equation. 376 + -64x + -376 + x2 = 0 + -376 Reorder the terms: 376 + -376 + -64x + x2 = 0 + -376 Combine like terms: 376 + -376 = 0 0 + -64x + x2 = 0 + -376 -64x + x2 = 0 + -376 Combine like terms: 0 + -376 = -376 -64x + x2 = -376 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 = -376 + 1024 Reorder the terms: 1024 + -64x + x2 = -376 + 1024 Combine like terms: -376 + 1024 = 648 1024 + -64x + x2 = 648 Factor a perfect square on the left side: (x + -32)(x + -32) = 648 Calculate the square root of the right side: 25.455844123 Break this problem into two subproblems by setting (x + -32) equal to 25.455844123 and -25.455844123.Subproblem 1
x + -32 = 25.455844123 Simplifying x + -32 = 25.455844123 Reorder the terms: -32 + x = 25.455844123 Solving -32 + x = 25.455844123 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 = 25.455844123 + 32 Combine like terms: -32 + 32 = 0 0 + x = 25.455844123 + 32 x = 25.455844123 + 32 Combine like terms: 25.455844123 + 32 = 57.455844123 x = 57.455844123 Simplifying x = 57.455844123Subproblem 2
x + -32 = -25.455844123 Simplifying x + -32 = -25.455844123 Reorder the terms: -32 + x = -25.455844123 Solving -32 + x = -25.455844123 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 = -25.455844123 + 32 Combine like terms: -32 + 32 = 0 0 + x = -25.455844123 + 32 x = -25.455844123 + 32 Combine like terms: -25.455844123 + 32 = 6.544155877 x = 6.544155877 Simplifying x = 6.544155877Solution
The solution to the problem is based on the solutions from the subproblems. x = {57.455844123, 6.544155877}
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