x(5x-4)=2

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Solution for x(5x-4)=2 equation:


Simplifying
x(5x + -4) = 2

Reorder the terms:
x(-4 + 5x) = 2
(-4 * x + 5x * x) = 2
(-4x + 5x2) = 2

Solving
-4x + 5x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + -4x + 5x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -4x + 5x2 = 0

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

Divide each side by '5'.
-0.4 + -0.8x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -0.8x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -0.8x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -0.8x + x2 = 0 + 0.4
-0.8x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-0.8x + x2 = 0.4

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = 0.4 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = 0.4 + 0.16

Combine like terms: 0.4 + 0.16 = 0.56
0.16 + -0.8x + x2 = 0.56

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 0.56

Calculate the square root of the right side: 0.748331477

Break this problem into two subproblems by setting 
(x + -0.4) equal to 0.748331477 and -0.748331477.

Subproblem 1

x + -0.4 = 0.748331477 Simplifying x + -0.4 = 0.748331477 Reorder the terms: -0.4 + x = 0.748331477 Solving -0.4 + x = 0.748331477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.748331477 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.748331477 + 0.4 x = 0.748331477 + 0.4 Combine like terms: 0.748331477 + 0.4 = 1.148331477 x = 1.148331477 Simplifying x = 1.148331477

Subproblem 2

x + -0.4 = -0.748331477 Simplifying x + -0.4 = -0.748331477 Reorder the terms: -0.4 + x = -0.748331477 Solving -0.4 + x = -0.748331477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -0.748331477 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.748331477 + 0.4 x = -0.748331477 + 0.4 Combine like terms: -0.748331477 + 0.4 = -0.348331477 x = -0.348331477 Simplifying x = -0.348331477

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.148331477, -0.348331477}

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