8x^2+64x=512

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Solution for 8x^2+64x=512 equation:


Simplifying
8x2 + 64x = 512

Reorder the terms:
64x + 8x2 = 512

Solving
64x + 8x2 = 512

Solving for variable 'x'.

Reorder the terms:
-512 + 64x + 8x2 = 512 + -512

Combine like terms: 512 + -512 = 0
-512 + 64x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-64 + 8x + x2) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(-64 + 8x + x2)' equal to zero and attempt to solve: Simplifying -64 + 8x + x2 = 0 Solving -64 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 8x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 8x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 8x + x2 = 0 + 64 8x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 8x + x2 = 64 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 64 + 16 Reorder the terms: 16 + 8x + x2 = 64 + 16 Combine like terms: 64 + 16 = 80 16 + 8x + x2 = 80 Factor a perfect square on the left side: (x + 4)(x + 4) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + 4) equal to 8.94427191 and -8.94427191.

Subproblem 1

x + 4 = 8.94427191 Simplifying x + 4 = 8.94427191 Reorder the terms: 4 + x = 8.94427191 Solving 4 + x = 8.94427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 8.94427191 + -4 Combine like terms: 4 + -4 = 0 0 + x = 8.94427191 + -4 x = 8.94427191 + -4 Combine like terms: 8.94427191 + -4 = 4.94427191 x = 4.94427191 Simplifying x = 4.94427191

Subproblem 2

x + 4 = -8.94427191 Simplifying x + 4 = -8.94427191 Reorder the terms: 4 + x = -8.94427191 Solving 4 + x = -8.94427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -8.94427191 + -4 Combine like terms: 4 + -4 = 0 0 + x = -8.94427191 + -4 x = -8.94427191 + -4 Combine like terms: -8.94427191 + -4 = -12.94427191 x = -12.94427191 Simplifying x = -12.94427191

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.94427191, -12.94427191}

Solution

x = {4.94427191, -12.94427191}

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