4x(x+38)=2x+47

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Solution for 4x(x+38)=2x+47 equation:


Simplifying
4x(x + 38) = 2x + 47

Reorder the terms:
4x(38 + x) = 2x + 47
(38 * 4x + x * 4x) = 2x + 47
(152x + 4x2) = 2x + 47

Reorder the terms:
152x + 4x2 = 47 + 2x

Solving
152x + 4x2 = 47 + 2x

Solving for variable 'x'.

Reorder the terms:
-47 + 152x + -2x + 4x2 = 47 + 2x + -47 + -2x

Combine like terms: 152x + -2x = 150x
-47 + 150x + 4x2 = 47 + 2x + -47 + -2x

Reorder the terms:
-47 + 150x + 4x2 = 47 + -47 + 2x + -2x

Combine like terms: 47 + -47 = 0
-47 + 150x + 4x2 = 0 + 2x + -2x
-47 + 150x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-47 + 150x + 4x2 = 0

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

Divide each side by '4'.
-11.75 + 37.5x + x2 = 0

Move the constant term to the right:

Add '11.75' to each side of the equation.
-11.75 + 37.5x + 11.75 + x2 = 0 + 11.75

Reorder the terms:
-11.75 + 11.75 + 37.5x + x2 = 0 + 11.75

Combine like terms: -11.75 + 11.75 = 0.00
0.00 + 37.5x + x2 = 0 + 11.75
37.5x + x2 = 0 + 11.75

Combine like terms: 0 + 11.75 = 11.75
37.5x + x2 = 11.75

The x term is 37.5x.  Take half its coefficient (18.75).
Square it (351.5625) and add it to both sides.

Add '351.5625' to each side of the equation.
37.5x + 351.5625 + x2 = 11.75 + 351.5625

Reorder the terms:
351.5625 + 37.5x + x2 = 11.75 + 351.5625

Combine like terms: 11.75 + 351.5625 = 363.3125
351.5625 + 37.5x + x2 = 363.3125

Factor a perfect square on the left side:
(x + 18.75)(x + 18.75) = 363.3125

Calculate the square root of the right side: 19.060758117

Break this problem into two subproblems by setting 
(x + 18.75) equal to 19.060758117 and -19.060758117.

Subproblem 1

x + 18.75 = 19.060758117 Simplifying x + 18.75 = 19.060758117 Reorder the terms: 18.75 + x = 19.060758117 Solving 18.75 + x = 19.060758117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.75' to each side of the equation. 18.75 + -18.75 + x = 19.060758117 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + x = 19.060758117 + -18.75 x = 19.060758117 + -18.75 Combine like terms: 19.060758117 + -18.75 = 0.310758117 x = 0.310758117 Simplifying x = 0.310758117

Subproblem 2

x + 18.75 = -19.060758117 Simplifying x + 18.75 = -19.060758117 Reorder the terms: 18.75 + x = -19.060758117 Solving 18.75 + x = -19.060758117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.75' to each side of the equation. 18.75 + -18.75 + x = -19.060758117 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + x = -19.060758117 + -18.75 x = -19.060758117 + -18.75 Combine like terms: -19.060758117 + -18.75 = -37.810758117 x = -37.810758117 Simplifying x = -37.810758117

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.310758117, -37.810758117}

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