7x^2+28x-42=0

Solution for 7x^2+28x-42=0 equation:

Simplifying
7x2 + 28x + -42 = 0

Reorder the terms:
-42 + 28x + 7x2 = 0

Solving
-42 + 28x + 7x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-6 + 4x + x2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-6 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-6 + 4x + x2 = 0

Solving
-6 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 4x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 4x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 4x + x2 = 0 + 6
4x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
4x + x2 = 6

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 6 + 4

Reorder the terms:
4 + 4x + x2 = 6 + 4

Combine like terms: 6 + 4 = 10
4 + 4x + x2 = 10

Factor a perfect square on the left side:
(x + 2)(x + 2) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 2) equal to 3.16227766 and -3.16227766.

Subproblem 1
x + 2 = 3.16227766

Simplifying
x + 2 = 3.16227766

Reorder the terms:
2 + x = 3.16227766

Solving
2 + x = 3.16227766

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 3.16227766 + -2

Combine like terms: 2 + -2 = 0
0 + x = 3.16227766 + -2
x = 3.16227766 + -2

Combine like terms: 3.16227766 + -2 = 1.16227766
x = 1.16227766

Simplifying
x = 1.16227766

Subproblem 2
x + 2 = -3.16227766

Simplifying
x + 2 = -3.16227766

Reorder the terms:
2 + x = -3.16227766

Solving
2 + x = -3.16227766

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -3.16227766 + -2

Combine like terms: 2 + -2 = 0
0 + x = -3.16227766 + -2
x = -3.16227766 + -2

Combine like terms: -3.16227766 + -2 = -5.16227766
x = -5.16227766

Simplifying
x = -5.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.16227766, -5.16227766}
Solution
x = {1.16227766, -5.16227766}