-4x^2+20x-7=0

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Solution for -4x^2+20x-7=0 equation: 


Simplifying
-4x2 + 20x + -7 = 0

Reorder the terms:
-7 + 20x + -4x2 = 0

Solving
-7 + 20x + -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'.
1.75 + -5x + x2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + -5x + -1.75 + x2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + -5x + x2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + -5x + x2 = 0 + -1.75
-5x + x2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
-5x + x2 = -1.75

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -1.75 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -1.75 + 6.25

Combine like terms: -1.75 + 6.25 = 4.5
6.25 + -5x + x2 = 4.5

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.121320344 and -2.121320344.


Subproblem 1
x + -2.5 = 2.121320344

Simplifying
x + -2.5 = 2.121320344

Reorder the terms:
-2.5 + x = 2.121320344

Solving
-2.5 + x = 2.121320344

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 2.121320344 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.121320344 + 2.5
x = 2.121320344 + 2.5

Combine like terms: 2.121320344 + 2.5 = 4.621320344
x = 4.621320344

Simplifying
x = 4.621320344


Subproblem 2
x + -2.5 = -2.121320344

Simplifying
x + -2.5 = -2.121320344

Reorder the terms:
-2.5 + x = -2.121320344

Solving
-2.5 + x = -2.121320344

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -2.121320344 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.121320344 + 2.5
x = -2.121320344 + 2.5

Combine like terms: -2.121320344 + 2.5 = 0.378679656
x = 0.378679656

Simplifying
x = 0.378679656


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.621320344, 0.378679656}

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