2x(5x+7)=7

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Solution for 2x(5x+7)=7 equation: 


Simplifying
2x(5x + 7) = 7

Reorder the terms:
2x(7 + 5x) = 7
(7 * 2x + 5x * 2x) = 7
(14x + 10x2) = 7

Solving
14x + 10x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + 14x + 10x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 14x + 10x2 = 0

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

Divide each side by '10'.
-0.7 + 1.4x + x2 = 0.0

Move the constant term to the right:

Add '0.7' to each side of the equation.
-0.7 + 1.4x + 0.7 + x2 = 0.0 + 0.7

Reorder the terms:
-0.7 + 0.7 + 1.4x + x2 = 0.0 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + 1.4x + x2 = 0.0 + 0.7
1.4x + x2 = 0.0 + 0.7

Combine like terms: 0.0 + 0.7 = 0.7
1.4x + x2 = 0.7

The x term is 1.4x.  Take half its coefficient (0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
1.4x + 0.49 + x2 = 0.7 + 0.49

Reorder the terms:
0.49 + 1.4x + x2 = 0.7 + 0.49

Combine like terms: 0.7 + 0.49 = 1.19
0.49 + 1.4x + x2 = 1.19

Factor a perfect square on the left side:
(x + 0.7)(x + 0.7) = 1.19

Calculate the square root of the right side: 1.090871211

Break this problem into two subproblems by setting 
(x + 0.7) equal to 1.090871211 and -1.090871211.


Subproblem 1
x + 0.7 = 1.090871211

Simplifying
x + 0.7 = 1.090871211

Reorder the terms:
0.7 + x = 1.090871211

Solving
0.7 + x = 1.090871211

Solving for variable 'x'.

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

Add '-0.7' to each side of the equation.
0.7 + -0.7 + x = 1.090871211 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + x = 1.090871211 + -0.7
x = 1.090871211 + -0.7

Combine like terms: 1.090871211 + -0.7 = 0.390871211
x = 0.390871211

Simplifying
x = 0.390871211


Subproblem 2
x + 0.7 = -1.090871211

Simplifying
x + 0.7 = -1.090871211

Reorder the terms:
0.7 + x = -1.090871211

Solving
0.7 + x = -1.090871211

Solving for variable 'x'.

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

Add '-0.7' to each side of the equation.
0.7 + -0.7 + x = -1.090871211 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + x = -1.090871211 + -0.7
x = -1.090871211 + -0.7

Combine like terms: -1.090871211 + -0.7 = -1.790871211
x = -1.790871211

Simplifying
x = -1.790871211


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.390871211, -1.790871211}

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