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Simplifying 0 = x2 + -64x + -512 Reorder the terms: 0 = -512 + -64x + x2 Solving 0 = -512 + -64x + x2 Solving for variable 'x'. Combine like terms: 0 + 512 = 512 512 + 64x + -1x2 = -512 + -64x + x2 + 512 + 64x + -1x2 Reorder the terms: 512 + 64x + -1x2 = -512 + 512 + -64x + 64x + x2 + -1x2 Combine like terms: -512 + 512 = 0 512 + 64x + -1x2 = 0 + -64x + 64x + x2 + -1x2 512 + 64x + -1x2 = -64x + 64x + x2 + -1x2 Combine like terms: -64x + 64x = 0 512 + 64x + -1x2 = 0 + x2 + -1x2 512 + 64x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 512 + 64x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -512 + -64x + x2 = 0 Move the constant term to the right: Add '512' to each side of the equation. -512 + -64x + 512 + x2 = 0 + 512 Reorder the terms: -512 + 512 + -64x + x2 = 0 + 512 Combine like terms: -512 + 512 = 0 0 + -64x + x2 = 0 + 512 -64x + x2 = 0 + 512 Combine like terms: 0 + 512 = 512 -64x + x2 = 512 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 = 512 + 1024 Reorder the terms: 1024 + -64x + x2 = 512 + 1024 Combine like terms: 512 + 1024 = 1536 1024 + -64x + x2 = 1536 Factor a perfect square on the left side: (x + -32)(x + -32) = 1536 Calculate the square root of the right side: 39.191835885 Break this problem into two subproblems by setting (x + -32) equal to 39.191835885 and -39.191835885.Subproblem 1
x + -32 = 39.191835885 Simplifying x + -32 = 39.191835885 Reorder the terms: -32 + x = 39.191835885 Solving -32 + x = 39.191835885 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 = 39.191835885 + 32 Combine like terms: -32 + 32 = 0 0 + x = 39.191835885 + 32 x = 39.191835885 + 32 Combine like terms: 39.191835885 + 32 = 71.191835885 x = 71.191835885 Simplifying x = 71.191835885Subproblem 2
x + -32 = -39.191835885 Simplifying x + -32 = -39.191835885 Reorder the terms: -32 + x = -39.191835885 Solving -32 + x = -39.191835885 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 = -39.191835885 + 32 Combine like terms: -32 + 32 = 0 0 + x = -39.191835885 + 32 x = -39.191835885 + 32 Combine like terms: -39.191835885 + 32 = -7.191835885 x = -7.191835885 Simplifying x = -7.191835885Solution
The solution to the problem is based on the solutions from the subproblems. x = {71.191835885, -7.191835885}
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