x^2-8x=-9.8

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Solution for x^2-8x=-9.8 equation: 


Simplifying
x2 + -8x = -9.8

Reorder the terms:
-8x + x2 = -9.8

Solving
-8x + x2 = -9.8

Solving for variable 'x'.

Reorder the terms:
9.8 + -8x + x2 = -9.8 + 9.8

Combine like terms: -9.8 + 9.8 = 0.0
9.8 + -8x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '-9.8' to each side of the equation.
9.8 + -8x + -9.8 + x2 = 0.0 + -9.8

Reorder the terms:
9.8 + -9.8 + -8x + x2 = 0.0 + -9.8

Combine like terms: 9.8 + -9.8 = 0.0
0.0 + -8x + x2 = 0.0 + -9.8
-8x + x2 = 0.0 + -9.8

Combine like terms: 0.0 + -9.8 = -9.8
-8x + x2 = -9.8

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 = -9.8 + 16

Reorder the terms:
16 + -8x + x2 = -9.8 + 16

Combine like terms: -9.8 + 16 = 6.2
16 + -8x + x2 = 6.2

Factor a perfect square on the left side:
(x + -4)(x + -4) = 6.2

Calculate the square root of the right side: 2.48997992

Break this problem into two subproblems by setting 
(x + -4) equal to 2.48997992 and -2.48997992.


Subproblem 1
x + -4 = 2.48997992

Simplifying
x + -4 = 2.48997992

Reorder the terms:
-4 + x = 2.48997992

Solving
-4 + x = 2.48997992

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 = 2.48997992 + 4

Combine like terms: -4 + 4 = 0
0 + x = 2.48997992 + 4
x = 2.48997992 + 4

Combine like terms: 2.48997992 + 4 = 6.48997992
x = 6.48997992

Simplifying
x = 6.48997992


Subproblem 2
x + -4 = -2.48997992

Simplifying
x + -4 = -2.48997992

Reorder the terms:
-4 + x = -2.48997992

Solving
-4 + x = -2.48997992

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 = -2.48997992 + 4

Combine like terms: -4 + 4 = 0
0 + x = -2.48997992 + 4
x = -2.48997992 + 4

Combine like terms: -2.48997992 + 4 = 1.51002008
x = 1.51002008

Simplifying
x = 1.51002008


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.48997992, 1.51002008}

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