-0.25x^2+5x-7=0

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Solution for -0.25x^2+5x-7=0 equation: 


Simplifying
-0.25x2 + 5x + -7 = 0

Reorder the terms:
-7 + 5x + -0.25x2 = 0

Solving
-7 + 5x + -0.25x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.25 the coefficient of the squared term: 

Divide each side by '-0.25'.
28 + -20x + x2 = 0

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -20x + -28 + x2 = 0 + -28

Reorder the terms:
28 + -28 + -20x + x2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -20x + x2 = 0 + -28
-20x + x2 = 0 + -28

Combine like terms: 0 + -28 = -28
-20x + x2 = -28

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -28 + 100

Reorder the terms:
100 + -20x + x2 = -28 + 100

Combine like terms: -28 + 100 = 72
100 + -20x + x2 = 72

Factor a perfect square on the left side:
(x + -10)(x + -10) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(x + -10) equal to 8.485281374 and -8.485281374.


Subproblem 1
x + -10 = 8.485281374

Simplifying
x + -10 = 8.485281374

Reorder the terms:
-10 + x = 8.485281374

Solving
-10 + x = 8.485281374

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 8.485281374 + 10

Combine like terms: -10 + 10 = 0
0 + x = 8.485281374 + 10
x = 8.485281374 + 10

Combine like terms: 8.485281374 + 10 = 18.485281374
x = 18.485281374

Simplifying
x = 18.485281374


Subproblem 2
x + -10 = -8.485281374

Simplifying
x + -10 = -8.485281374

Reorder the terms:
-10 + x = -8.485281374

Solving
-10 + x = -8.485281374

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -8.485281374 + 10

Combine like terms: -10 + 10 = 0
0 + x = -8.485281374 + 10
x = -8.485281374 + 10

Combine like terms: -8.485281374 + 10 = 1.514718626
x = 1.514718626

Simplifying
x = 1.514718626


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.485281374, 1.514718626}

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