4x-0.1*(x^2)=8

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Solution for 4x-0.1*(x^2)=8 equation:


Simplifying
4x + -0.1(x2) = 8

Solving
4x + -0.1x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + 4x + -0.1x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 4x + -0.1x2 = 0

Begin completing the square.  Divide all terms by
-0.1 the coefficient of the squared term: 

Divide each side by '-0.1'.
80 + -40x + x2 = 0

Move the constant term to the right:

Add '-80' to each side of the equation.
80 + -40x + -80 + x2 = 0 + -80

Reorder the terms:
80 + -80 + -40x + x2 = 0 + -80

Combine like terms: 80 + -80 = 0
0 + -40x + x2 = 0 + -80
-40x + x2 = 0 + -80

Combine like terms: 0 + -80 = -80
-40x + x2 = -80

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = -80 + 400

Reorder the terms:
400 + -40x + x2 = -80 + 400

Combine like terms: -80 + 400 = 320
400 + -40x + x2 = 320

Factor a perfect square on the left side:
(x + -20)(x + -20) = 320

Calculate the square root of the right side: 17.88854382

Break this problem into two subproblems by setting 
(x + -20) equal to 17.88854382 and -17.88854382.

Subproblem 1

x + -20 = 17.88854382 Simplifying x + -20 = 17.88854382 Reorder the terms: -20 + x = 17.88854382 Solving -20 + x = 17.88854382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 17.88854382 + 20 Combine like terms: -20 + 20 = 0 0 + x = 17.88854382 + 20 x = 17.88854382 + 20 Combine like terms: 17.88854382 + 20 = 37.88854382 x = 37.88854382 Simplifying x = 37.88854382

Subproblem 2

x + -20 = -17.88854382 Simplifying x + -20 = -17.88854382 Reorder the terms: -20 + x = -17.88854382 Solving -20 + x = -17.88854382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -17.88854382 + 20 Combine like terms: -20 + 20 = 0 0 + x = -17.88854382 + 20 x = -17.88854382 + 20 Combine like terms: -17.88854382 + 20 = 2.11145618 x = 2.11145618 Simplifying x = 2.11145618

Solution

The solution to the problem is based on the solutions from the subproblems. x = {37.88854382, 2.11145618}

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