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Simplifying
x2 + 7x + -3 = 0

Reorder the terms:
-3 + 7x + x2 = 0

Solving
-3 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 7x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 7x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 7x + x2 = 0 + 3
7x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
7x + x2 = 3

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 3 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 3 + 12.25

Combine like terms: 3 + 12.25 = 15.25
12.25 + 7x + x2 = 15.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.905124838 and -3.905124838.

Subproblem 1

x + 3.5 = 3.905124838 Simplifying x + 3.5 = 3.905124838 Reorder the terms: 3.5 + x = 3.905124838 Solving 3.5 + x = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.905124838 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.905124838 + -3.5 x = 3.905124838 + -3.5 Combine like terms: 3.905124838 + -3.5 = 0.405124838 x = 0.405124838 Simplifying x = 0.405124838

Subproblem 2

x + 3.5 = -3.905124838 Simplifying x + 3.5 = -3.905124838 Reorder the terms: 3.5 + x = -3.905124838 Solving 3.5 + x = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.905124838 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.905124838 + -3.5 x = -3.905124838 + -3.5 Combine like terms: -3.905124838 + -3.5 = -7.405124838 x = -7.405124838 Simplifying x = -7.405124838

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.405124838, -7.405124838}
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