5x*5x+6x-2=0

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Solution for 5x*5x+6x-2=0 equation:


Simplifying
5x * 5x + 6x + -2 = 0

Reorder the terms for easier multiplication:
5 * 5x * x + 6x + -2 = 0

Multiply 5 * 5
25x * x + 6x + -2 = 0

Multiply x * x
25x2 + 6x + -2 = 0

Reorder the terms:
-2 + 6x + 25x2 = 0

Solving
-2 + 6x + 25x2 = 0

Solving for variable 'x'.

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

Divide each side by '25'.
-0.08 + 0.24x + x2 = 0

Move the constant term to the right:

Add '0.08' to each side of the equation.
-0.08 + 0.24x + 0.08 + x2 = 0 + 0.08

Reorder the terms:
-0.08 + 0.08 + 0.24x + x2 = 0 + 0.08

Combine like terms: -0.08 + 0.08 = 0.00
0.00 + 0.24x + x2 = 0 + 0.08
0.24x + x2 = 0 + 0.08

Combine like terms: 0 + 0.08 = 0.08
0.24x + x2 = 0.08

The x term is 0.24x.  Take half its coefficient (0.12).
Square it (0.0144) and add it to both sides.

Add '0.0144' to each side of the equation.
0.24x + 0.0144 + x2 = 0.08 + 0.0144

Reorder the terms:
0.0144 + 0.24x + x2 = 0.08 + 0.0144

Combine like terms: 0.08 + 0.0144 = 0.0944
0.0144 + 0.24x + x2 = 0.0944

Factor a perfect square on the left side:
(x + 0.12)(x + 0.12) = 0.0944

Calculate the square root of the right side: 0.30724583

Break this problem into two subproblems by setting 
(x + 0.12) equal to 0.30724583 and -0.30724583.

Subproblem 1

x + 0.12 = 0.30724583 Simplifying x + 0.12 = 0.30724583 Reorder the terms: 0.12 + x = 0.30724583 Solving 0.12 + x = 0.30724583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.12' to each side of the equation. 0.12 + -0.12 + x = 0.30724583 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + x = 0.30724583 + -0.12 x = 0.30724583 + -0.12 Combine like terms: 0.30724583 + -0.12 = 0.18724583 x = 0.18724583 Simplifying x = 0.18724583

Subproblem 2

x + 0.12 = -0.30724583 Simplifying x + 0.12 = -0.30724583 Reorder the terms: 0.12 + x = -0.30724583 Solving 0.12 + x = -0.30724583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.12' to each side of the equation. 0.12 + -0.12 + x = -0.30724583 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + x = -0.30724583 + -0.12 x = -0.30724583 + -0.12 Combine like terms: -0.30724583 + -0.12 = -0.42724583 x = -0.42724583 Simplifying x = -0.42724583

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.18724583, -0.42724583}

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