x^2-8x=5

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Solution for x^2-8x=5 equation:


Simplifying
x2 + -8x = 5

Reorder the terms:
-8x + x2 = 5

Solving
-8x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + -8x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -8x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -8x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -8x + x2 = 0 + 5
-8x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-8x + x2 = 5

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 = 5 + 16

Reorder the terms:
16 + -8x + x2 = 5 + 16

Combine like terms: 5 + 16 = 21
16 + -8x + x2 = 21

Factor a perfect square on the left side:
(x + -4)(x + -4) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x + -4) equal to 4.582575695 and -4.582575695.

Subproblem 1

x + -4 = 4.582575695 Simplifying x + -4 = 4.582575695 Reorder the terms: -4 + x = 4.582575695 Solving -4 + x = 4.582575695 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 = 4.582575695 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.582575695 + 4 x = 4.582575695 + 4 Combine like terms: 4.582575695 + 4 = 8.582575695 x = 8.582575695 Simplifying x = 8.582575695

Subproblem 2

x + -4 = -4.582575695 Simplifying x + -4 = -4.582575695 Reorder the terms: -4 + x = -4.582575695 Solving -4 + x = -4.582575695 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 = -4.582575695 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.582575695 + 4 x = -4.582575695 + 4 Combine like terms: -4.582575695 + 4 = -0.582575695 x = -0.582575695 Simplifying x = -0.582575695

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.582575695, -0.582575695}

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