x(28x+23)=4

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Solution for x(28x+23)=4 equation:


Simplifying
x(28x + 23) = 4

Reorder the terms:
x(23 + 28x) = 4
(23 * x + 28x * x) = 4
(23x + 28x2) = 4

Solving
23x + 28x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 23x + 28x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 23x + 28x2 = 0

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

Divide each side by '28'.
-0.1428571429 + 0.8214285714x + x2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + 0.8214285714x + 0.1428571429 + x2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + 0.8214285714x + x2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + 0.8214285714x + x2 = 0 + 0.1428571429
0.8214285714x + x2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
0.8214285714x + x2 = 0.1428571429

The x term is 0.8214285714x.  Take half its coefficient (0.4107142857).
Square it (0.1686862245) and add it to both sides.

Add '0.1686862245' to each side of the equation.
0.8214285714x + 0.1686862245 + x2 = 0.1428571429 + 0.1686862245

Reorder the terms:
0.1686862245 + 0.8214285714x + x2 = 0.1428571429 + 0.1686862245

Combine like terms: 0.1428571429 + 0.1686862245 = 0.3115433674
0.1686862245 + 0.8214285714x + x2 = 0.3115433674

Factor a perfect square on the left side:
(x + 0.4107142857)(x + 0.4107142857) = 0.3115433674

Calculate the square root of the right side: 0.5581607

Break this problem into two subproblems by setting 
(x + 0.4107142857) equal to 0.5581607 and -0.5581607.

Subproblem 1

x + 0.4107142857 = 0.5581607 Simplifying x + 0.4107142857 = 0.5581607 Reorder the terms: 0.4107142857 + x = 0.5581607 Solving 0.4107142857 + x = 0.5581607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4107142857' to each side of the equation. 0.4107142857 + -0.4107142857 + x = 0.5581607 + -0.4107142857 Combine like terms: 0.4107142857 + -0.4107142857 = 0.0000000000 0.0000000000 + x = 0.5581607 + -0.4107142857 x = 0.5581607 + -0.4107142857 Combine like terms: 0.5581607 + -0.4107142857 = 0.1474464143 x = 0.1474464143 Simplifying x = 0.1474464143

Subproblem 2

x + 0.4107142857 = -0.5581607 Simplifying x + 0.4107142857 = -0.5581607 Reorder the terms: 0.4107142857 + x = -0.5581607 Solving 0.4107142857 + x = -0.5581607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4107142857' to each side of the equation. 0.4107142857 + -0.4107142857 + x = -0.5581607 + -0.4107142857 Combine like terms: 0.4107142857 + -0.4107142857 = 0.0000000000 0.0000000000 + x = -0.5581607 + -0.4107142857 x = -0.5581607 + -0.4107142857 Combine like terms: -0.5581607 + -0.4107142857 = -0.9688749857 x = -0.9688749857 Simplifying x = -0.9688749857

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.1474464143, -0.9688749857}

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