1.4x(x+3)=5.32

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Solution for 1.4x(x+3)=5.32 equation: 


Simplifying
1.4x(x + 3) = 5.32

Reorder the terms:
1.4x(3 + x) = 5.32
(3 * 1.4x + x * 1.4x) = 5.32
(4.2x + 1.4x2) = 5.32

Solving
4.2x + 1.4x2 = 5.32

Solving for variable 'x'.

Reorder the terms:
-5.32 + 4.2x + 1.4x2 = 5.32 + -5.32

Combine like terms: 5.32 + -5.32 = 0.00
-5.32 + 4.2x + 1.4x2 = 0.00

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

Divide each side by '1.4'.
-3.8 + 3x + x2 = 0.0

Move the constant term to the right:

Add '3.8' to each side of the equation.
-3.8 + 3x + 3.8 + x2 = 0.0 + 3.8

Reorder the terms:
-3.8 + 3.8 + 3x + x2 = 0.0 + 3.8

Combine like terms: -3.8 + 3.8 = 0.0
0.0 + 3x + x2 = 0.0 + 3.8
3x + x2 = 0.0 + 3.8

Combine like terms: 0.0 + 3.8 = 3.8
3x + x2 = 3.8

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 3.8 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 3.8 + 2.25

Combine like terms: 3.8 + 2.25 = 6.05
2.25 + 3x + x2 = 6.05

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 6.05

Calculate the square root of the right side: 2.459674775

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.459674775 and -2.459674775.


Subproblem 1
x + 1.5 = 2.459674775

Simplifying
x + 1.5 = 2.459674775

Reorder the terms:
1.5 + x = 2.459674775

Solving
1.5 + x = 2.459674775

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 2.459674775 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2.459674775 + -1.5
x = 2.459674775 + -1.5

Combine like terms: 2.459674775 + -1.5 = 0.959674775
x = 0.959674775

Simplifying
x = 0.959674775


Subproblem 2
x + 1.5 = -2.459674775

Simplifying
x + 1.5 = -2.459674775

Reorder the terms:
1.5 + x = -2.459674775

Solving
1.5 + x = -2.459674775

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -2.459674775 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2.459674775 + -1.5
x = -2.459674775 + -1.5

Combine like terms: -2.459674775 + -1.5 = -3.959674775
x = -3.959674775

Simplifying
x = -3.959674775


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.959674775, -3.959674775}

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