5x(5x)+3x=2

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Solution for 5x(5x)+3x=2 equation:


Simplifying
5x(5x) + 3x = 2

Remove parenthesis around (5x)
5x * 5x + 3x = 2

Reorder the terms for easier multiplication:
5 * 5x * x + 3x = 2

Multiply 5 * 5
25x * x + 3x = 2

Multiply x * x
25x2 + 3x = 2

Reorder the terms:
3x + 25x2 = 2

Solving
3x + 25x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + 3x + 25x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 3x + 25x2 = 0

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

Divide each side by '25'.
-0.08 + 0.12x + x2 = 0

Move the constant term to the right:

Add '0.08' to each side of the equation.
-0.08 + 0.12x + 0.08 + x2 = 0 + 0.08

Reorder the terms:
-0.08 + 0.08 + 0.12x + x2 = 0 + 0.08

Combine like terms: -0.08 + 0.08 = 0.00
0.00 + 0.12x + x2 = 0 + 0.08
0.12x + x2 = 0 + 0.08

Combine like terms: 0 + 0.08 = 0.08
0.12x + x2 = 0.08

The x term is 0.12x.  Take half its coefficient (0.06).
Square it (0.0036) and add it to both sides.

Add '0.0036' to each side of the equation.
0.12x + 0.0036 + x2 = 0.08 + 0.0036

Reorder the terms:
0.0036 + 0.12x + x2 = 0.08 + 0.0036

Combine like terms: 0.08 + 0.0036 = 0.0836
0.0036 + 0.12x + x2 = 0.0836

Factor a perfect square on the left side:
(x + 0.06)(x + 0.06) = 0.0836

Calculate the square root of the right side: 0.289136646

Break this problem into two subproblems by setting 
(x + 0.06) equal to 0.289136646 and -0.289136646.

Subproblem 1

x + 0.06 = 0.289136646 Simplifying x + 0.06 = 0.289136646 Reorder the terms: 0.06 + x = 0.289136646 Solving 0.06 + x = 0.289136646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06' to each side of the equation. 0.06 + -0.06 + x = 0.289136646 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = 0.289136646 + -0.06 x = 0.289136646 + -0.06 Combine like terms: 0.289136646 + -0.06 = 0.229136646 x = 0.229136646 Simplifying x = 0.229136646

Subproblem 2

x + 0.06 = -0.289136646 Simplifying x + 0.06 = -0.289136646 Reorder the terms: 0.06 + x = -0.289136646 Solving 0.06 + x = -0.289136646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06' to each side of the equation. 0.06 + -0.06 + x = -0.289136646 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = -0.289136646 + -0.06 x = -0.289136646 + -0.06 Combine like terms: -0.289136646 + -0.06 = -0.349136646 x = -0.349136646 Simplifying x = -0.349136646

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.229136646, -0.349136646}

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