8x^2+28x+21=0

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Solution for 8x^2+28x+21=0 equation: 


Simplifying
8x2 + 28x + 21 = 0

Reorder the terms:
21 + 28x + 8x2 = 0

Solving
21 + 28x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
2.625 + 3.5x + x2 = 0

Move the constant term to the right:

Add '-2.625' to each side of the equation.
2.625 + 3.5x + -2.625 + x2 = 0 + -2.625

Reorder the terms:
2.625 + -2.625 + 3.5x + x2 = 0 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + 3.5x + x2 = 0 + -2.625
3.5x + x2 = 0 + -2.625

Combine like terms: 0 + -2.625 = -2.625
3.5x + x2 = -2.625

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = -2.625 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = -2.625 + 3.0625

Combine like terms: -2.625 + 3.0625 = 0.4375
3.0625 + 3.5x + x2 = 0.4375

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 0.4375

Calculate the square root of the right side: 0.661437828

Break this problem into two subproblems by setting 
(x + 1.75) equal to 0.661437828 and -0.661437828.


Subproblem 1
x + 1.75 = 0.661437828

Simplifying
x + 1.75 = 0.661437828

Reorder the terms:
1.75 + x = 0.661437828

Solving
1.75 + x = 0.661437828

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 0.661437828 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 0.661437828 + -1.75
x = 0.661437828 + -1.75

Combine like terms: 0.661437828 + -1.75 = -1.088562172
x = -1.088562172

Simplifying
x = -1.088562172


Subproblem 2
x + 1.75 = -0.661437828

Simplifying
x + 1.75 = -0.661437828

Reorder the terms:
1.75 + x = -0.661437828

Solving
1.75 + x = -0.661437828

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -0.661437828 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -0.661437828 + -1.75
x = -0.661437828 + -1.75

Combine like terms: -0.661437828 + -1.75 = -2.411437828
x = -2.411437828

Simplifying
x = -2.411437828


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.088562172, -2.411437828}

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