4x^2+21x-8=0

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Solution for 4x^2+21x-8=0 equation:


Simplifying
4x2 + 21x + -8 = 0

Reorder the terms:
-8 + 21x + 4x2 = 0

Solving
-8 + 21x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-2 + 5.25x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 5.25x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 5.25x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 5.25x + x2 = 0 + 2
5.25x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
5.25x + x2 = 2

The x term is 5.25x.  Take half its coefficient (2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
5.25x + 6.890625 + x2 = 2 + 6.890625

Reorder the terms:
6.890625 + 5.25x + x2 = 2 + 6.890625

Combine like terms: 2 + 6.890625 = 8.890625
6.890625 + 5.25x + x2 = 8.890625

Factor a perfect square on the left side:
(x + 2.625)(x + 2.625) = 8.890625

Calculate the square root of the right side: 2.98171511

Break this problem into two subproblems by setting 
(x + 2.625) equal to 2.98171511 and -2.98171511.


Subproblem 1
x + 2.625 = 2.98171511

Simplifying
x + 2.625 = 2.98171511

Reorder the terms:
2.625 + x = 2.98171511

Solving
2.625 + x = 2.98171511

Solving for variable 'x'.

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

Add '-2.625' to each side of the equation.
2.625 + -2.625 + x = 2.98171511 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + x = 2.98171511 + -2.625
x = 2.98171511 + -2.625

Combine like terms: 2.98171511 + -2.625 = 0.35671511
x = 0.35671511

Simplifying
x = 0.35671511


Subproblem 2
x + 2.625 = -2.98171511

Simplifying
x + 2.625 = -2.98171511

Reorder the terms:
2.625 + x = -2.98171511

Solving
2.625 + x = -2.98171511

Solving for variable 'x'.

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

Add '-2.625' to each side of the equation.
2.625 + -2.625 + x = -2.98171511 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + x = -2.98171511 + -2.625
x = -2.98171511 + -2.625

Combine like terms: -2.98171511 + -2.625 = -5.60671511
x = -5.60671511

Simplifying
x = -5.60671511


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.35671511, -5.60671511}

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