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Simplifying x2 + -64x + 584 = 0 Reorder the terms: 584 + -64x + x2 = 0 Solving 584 + -64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-584' to each side of the equation. 584 + -64x + -584 + x2 = 0 + -584 Reorder the terms: 584 + -584 + -64x + x2 = 0 + -584 Combine like terms: 584 + -584 = 0 0 + -64x + x2 = 0 + -584 -64x + x2 = 0 + -584 Combine like terms: 0 + -584 = -584 -64x + x2 = -584 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 = -584 + 1024 Reorder the terms: 1024 + -64x + x2 = -584 + 1024 Combine like terms: -584 + 1024 = 440 1024 + -64x + x2 = 440 Factor a perfect square on the left side: (x + -32)(x + -32) = 440 Calculate the square root of the right side: 20.976176963 Break this problem into two subproblems by setting (x + -32) equal to 20.976176963 and -20.976176963.Subproblem 1
x + -32 = 20.976176963 Simplifying x + -32 = 20.976176963 Reorder the terms: -32 + x = 20.976176963 Solving -32 + x = 20.976176963 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 = 20.976176963 + 32 Combine like terms: -32 + 32 = 0 0 + x = 20.976176963 + 32 x = 20.976176963 + 32 Combine like terms: 20.976176963 + 32 = 52.976176963 x = 52.976176963 Simplifying x = 52.976176963Subproblem 2
x + -32 = -20.976176963 Simplifying x + -32 = -20.976176963 Reorder the terms: -32 + x = -20.976176963 Solving -32 + x = -20.976176963 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 = -20.976176963 + 32 Combine like terms: -32 + 32 = 0 0 + x = -20.976176963 + 32 x = -20.976176963 + 32 Combine like terms: -20.976176963 + 32 = 11.023823037 x = 11.023823037 Simplifying x = 11.023823037Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.976176963, 11.023823037}
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