2x^2+8x-19.25=0

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Solution for 2x^2+8x-19.25=0 equation: 


Simplifying
2x2 + 8x + -19.25 = 0

Reorder the terms:
-19.25 + 8x + 2x2 = 0

Solving
-19.25 + 8x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-9.625 + 4x + x2 = 0

Move the constant term to the right:

Add '9.625' to each side of the equation.
-9.625 + 4x + 9.625 + x2 = 0 + 9.625

Reorder the terms:
-9.625 + 9.625 + 4x + x2 = 0 + 9.625

Combine like terms: -9.625 + 9.625 = 0.000
0.000 + 4x + x2 = 0 + 9.625
4x + x2 = 0 + 9.625

Combine like terms: 0 + 9.625 = 9.625
4x + x2 = 9.625

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 = 9.625 + 4

Reorder the terms:
4 + 4x + x2 = 9.625 + 4

Combine like terms: 9.625 + 4 = 13.625
4 + 4x + x2 = 13.625

Factor a perfect square on the left side:
(x + 2)(x + 2) = 13.625

Calculate the square root of the right side: 3.691205765

Break this problem into two subproblems by setting 
(x + 2) equal to 3.691205765 and -3.691205765.


Subproblem 1
x + 2 = 3.691205765

Simplifying
x + 2 = 3.691205765

Reorder the terms:
2 + x = 3.691205765

Solving
2 + x = 3.691205765

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 = 3.691205765 + -2

Combine like terms: 2 + -2 = 0
0 + x = 3.691205765 + -2
x = 3.691205765 + -2

Combine like terms: 3.691205765 + -2 = 1.691205765
x = 1.691205765

Simplifying
x = 1.691205765


Subproblem 2
x + 2 = -3.691205765

Simplifying
x + 2 = -3.691205765

Reorder the terms:
2 + x = -3.691205765

Solving
2 + x = -3.691205765

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 = -3.691205765 + -2

Combine like terms: 2 + -2 = 0
0 + x = -3.691205765 + -2
x = -3.691205765 + -2

Combine like terms: -3.691205765 + -2 = -5.691205765
x = -5.691205765

Simplifying
x = -5.691205765


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.691205765, -5.691205765}

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