5x^2+(0.2x)-2=0

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Solution for 5x^2+(0.2x)-2=0 equation:


Simplifying
5x2 + (0.2x) + -2 = 0

Reorder the terms:
-2 + (0.2x) + 5x2 = 0

Solving
-2 + (0.2x) + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-0.4 + (0.04x) + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + (0.04x) + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + (0.04x) + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + (0.04x) + x2 = 0 + 0.4
(0.04x) + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
(0.04x) + x2 = 0.4

The x term is (0.04x).  Take half its coefficient (0.02).
Square it (0.0004) and add it to both sides.

Add '0.0004' to each side of the equation.
(0.04x) + 0.0004 + x2 = 0.4 + 0.0004

Reorder the terms:
0.0004 + (0.04x) + x2 = 0.4 + 0.0004

Combine like terms: 0.4 + 0.0004 = 0.4004
0.0004 + (0.04x) + x2 = 0.4004

Factor a perfect square on the left side:
(x + 0.02)(x + 0.02) = 0.4004

Calculate the square root of the right side: 0.632771681

Break this problem into two subproblems by setting 
(x + 0.02) equal to 0.632771681 and -0.632771681.

Subproblem 1

x + 0.02 = 0.632771681 Simplifying x + 0.02 = 0.632771681 Reorder the terms: 0.02 + x = 0.632771681 Solving 0.02 + x = 0.632771681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02' to each side of the equation. 0.02 + -0.02 + x = 0.632771681 + -0.02 Combine like terms: 0.02 + -0.02 = 0.00 0.00 + x = 0.632771681 + -0.02 x = 0.632771681 + -0.02 Combine like terms: 0.632771681 + -0.02 = 0.612771681 x = 0.612771681 Simplifying x = 0.612771681

Subproblem 2

x + 0.02 = -0.632771681 Simplifying x + 0.02 = -0.632771681 Reorder the terms: 0.02 + x = -0.632771681 Solving 0.02 + x = -0.632771681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02' to each side of the equation. 0.02 + -0.02 + x = -0.632771681 + -0.02 Combine like terms: 0.02 + -0.02 = 0.00 0.00 + x = -0.632771681 + -0.02 x = -0.632771681 + -0.02 Combine like terms: -0.632771681 + -0.02 = -0.652771681 x = -0.652771681 Simplifying x = -0.652771681

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.612771681, -0.652771681}

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