x(5x+4)=4

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Solution for x(5x+4)=4 equation:


Simplifying
x(5x + 4) = 4

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

Solving
4x + 5x2 = 4

Solving for variable 'x'.

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

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

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

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

Move the constant term to the right:

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

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

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

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

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 = 0.8 + 0.16

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

Combine like terms: 0.8 + 0.16 = 0.96
0.16 + 0.8x + x2 = 0.96

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 0.96

Calculate the square root of the right side: 0.979795897

Break this problem into two subproblems by setting 
(x + 0.4) equal to 0.979795897 and -0.979795897.

Subproblem 1

x + 0.4 = 0.979795897 Simplifying x + 0.4 = 0.979795897 Reorder the terms: 0.4 + x = 0.979795897 Solving 0.4 + x = 0.979795897 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 = 0.979795897 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 0.979795897 + -0.4 x = 0.979795897 + -0.4 Combine like terms: 0.979795897 + -0.4 = 0.579795897 x = 0.579795897 Simplifying x = 0.579795897

Subproblem 2

x + 0.4 = -0.979795897 Simplifying x + 0.4 = -0.979795897 Reorder the terms: 0.4 + x = -0.979795897 Solving 0.4 + x = -0.979795897 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 = -0.979795897 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -0.979795897 + -0.4 x = -0.979795897 + -0.4 Combine like terms: -0.979795897 + -0.4 = -1.379795897 x = -1.379795897 Simplifying x = -1.379795897

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.579795897, -1.379795897}

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