(x-8)(x-0.1)=0

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Solution for (x-8)(x-0.1)=0 equation:


Simplifying
(x + -8)(x + -0.1) = 0

Reorder the terms:
(-8 + x)(x + -0.1) = 0

Reorder the terms:
(-8 + x)(-0.1 + x) = 0

Multiply (-8 + x) * (-0.1 + x)
(-8(-0.1 + x) + x(-0.1 + x)) = 0
((-0.1 * -8 + x * -8) + x(-0.1 + x)) = 0
((0.8 + -8x) + x(-0.1 + x)) = 0
(0.8 + -8x + (-0.1 * x + x * x)) = 0
(0.8 + -8x + (-0.1x + x2)) = 0

Combine like terms: -8x + -0.1x = -8.1x
(0.8 + -8.1x + x2) = 0

Solving
0.8 + -8.1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + -8.1x + -0.8 + x2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + -8.1x + x2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + -8.1x + x2 = 0 + -0.8
-8.1x + x2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
-8.1x + x2 = -0.8

The x term is -8.1x.  Take half its coefficient (-4.05).
Square it (16.4025) and add it to both sides.

Add '16.4025' to each side of the equation.
-8.1x + 16.4025 + x2 = -0.8 + 16.4025

Reorder the terms:
16.4025 + -8.1x + x2 = -0.8 + 16.4025

Combine like terms: -0.8 + 16.4025 = 15.6025
16.4025 + -8.1x + x2 = 15.6025

Factor a perfect square on the left side:
(x + -4.05)(x + -4.05) = 15.6025

Calculate the square root of the right side: 3.95

Break this problem into two subproblems by setting 
(x + -4.05) equal to 3.95 and -3.95.

Subproblem 1

x + -4.05 = 3.95 Simplifying x + -4.05 = 3.95 Reorder the terms: -4.05 + x = 3.95 Solving -4.05 + x = 3.95 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.05' to each side of the equation. -4.05 + 4.05 + x = 3.95 + 4.05 Combine like terms: -4.05 + 4.05 = 0.00 0.00 + x = 3.95 + 4.05 x = 3.95 + 4.05 Combine like terms: 3.95 + 4.05 = 8 x = 8 Simplifying x = 8

Subproblem 2

x + -4.05 = -3.95 Simplifying x + -4.05 = -3.95 Reorder the terms: -4.05 + x = -3.95 Solving -4.05 + x = -3.95 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.05' to each side of the equation. -4.05 + 4.05 + x = -3.95 + 4.05 Combine like terms: -4.05 + 4.05 = 0.00 0.00 + x = -3.95 + 4.05 x = -3.95 + 4.05 Combine like terms: -3.95 + 4.05 = 0.1 x = 0.1 Simplifying x = 0.1

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8, 0.1}

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