7x(2x+5)+3=0

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Solution for 7x(2x+5)+3=0 equation:


Simplifying
7x(2x + 5) + 3 = 0

Reorder the terms:
7x(5 + 2x) + 3 = 0
(5 * 7x + 2x * 7x) + 3 = 0
(35x + 14x2) + 3 = 0

Reorder the terms:
3 + 35x + 14x2 = 0

Solving
3 + 35x + 14x2 = 0

Solving for variable 'x'.

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

Divide each side by '14'.
0.2142857143 + 2.5x + x2 = 0

Move the constant term to the right:

Add '-0.2142857143' to each side of the equation.
0.2142857143 + 2.5x + -0.2142857143 + x2 = 0 + -0.2142857143

Reorder the terms:
0.2142857143 + -0.2142857143 + 2.5x + x2 = 0 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + 2.5x + x2 = 0 + -0.2142857143
2.5x + x2 = 0 + -0.2142857143

Combine like terms: 0 + -0.2142857143 = -0.2142857143
2.5x + x2 = -0.2142857143

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = -0.2142857143 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = -0.2142857143 + 1.5625

Combine like terms: -0.2142857143 + 1.5625 = 1.3482142857
1.5625 + 2.5x + x2 = 1.3482142857

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 1.3482142857

Calculate the square root of the right side: 1.1611263

Break this problem into two subproblems by setting 
(x + 1.25) equal to 1.1611263 and -1.1611263.

Subproblem 1

x + 1.25 = 1.1611263 Simplifying x + 1.25 = 1.1611263 Reorder the terms: 1.25 + x = 1.1611263 Solving 1.25 + x = 1.1611263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.1611263 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.1611263 + -1.25 x = 1.1611263 + -1.25 Combine like terms: 1.1611263 + -1.25 = -0.0888737 x = -0.0888737 Simplifying x = -0.0888737

Subproblem 2

x + 1.25 = -1.1611263 Simplifying x + 1.25 = -1.1611263 Reorder the terms: 1.25 + x = -1.1611263 Solving 1.25 + x = -1.1611263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.1611263 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.1611263 + -1.25 x = -1.1611263 + -1.25 Combine like terms: -1.1611263 + -1.25 = -2.4111263 x = -2.4111263 Simplifying x = -2.4111263

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.0888737, -2.4111263}

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