# Learn Interfaces by Building an Equation Solver - Step 53

### Tell us what’s happening:

i’m struggling to comprehend on how we add the new “piece” to our output_string, also how do we do form the string “solutions”

``````from abc import ABC, abstractmethod
import re

class Equation(ABC):
degree: int
type: str

def __init__(self, *args):
if (self.degree + 1) != len(args):
raise TypeError(
f"'Equation' object takes {self.degree + 1} positional arguments but {len(args)} were given"
)
if any(not isinstance(arg, (int, float)) for arg in args):
raise TypeError("Coefficients must be of type 'int' or 'float'")
if args[0] == 0:
raise ValueError("Highest degree coefficient must be different from zero")
self.coefficients = {(len(args) - n - 1): arg for n, arg in enumerate(args)}

def __init_subclass__(cls):
if not hasattr(cls, "degree"):
raise AttributeError(
f"Cannot create '{cls.__name__}' class: missing required attribute 'degree'"
)
if not hasattr(cls, "type"):
raise AttributeError(
f"Cannot create '{cls.__name__}' class: missing required attribute 'type'"
)

def __str__(self):
terms = []
for n, coefficient in self.coefficients.items():
if not coefficient:
continue
if n == 0:
terms.append(f'{coefficient:+}')
elif n == 1:
terms.append(f'{coefficient:+}x')
else:
terms.append(f"{coefficient:+}x**{n}")
equation_string = ' '.join(terms) + ' = 0'
return re.sub(r"(?<!\d)1(?=x)", "", equation_string.strip("+"))

@abstractmethod
def solve(self):
pass

@abstractmethod
def analyze(self):
pass

class LinearEquation(Equation):
degree = 1
type = 'Linear Equation'

def solve(self):
a, b = self.coefficients.values()
x = -b / a
return [x]

def analyze(self):
slope, intercept = self.coefficients.values()
return {'slope': slope, 'intercept': intercept}

degree = 2

def __init__(self, *args):
super().__init__(*args)
a, b, c = self.coefficients.values()
self.delta = b**2 - 4 * a * c

def solve(self):
if self.delta < 0:
return []
a, b, _ = self.coefficients.values()
x1 = (-b + (self.delta) ** 0.5) / (2 * a)
x2 = (-b - (self.delta) ** 0.5) / (2 * a)
if self.delta == 0:
return [x1]

return [x1, x2]

def analyze(self):
a, b, c = self.coefficients.values()
x = -b / (2 * a)
y = a * x**2 + b * x + c
if a > 0:
concavity = 'upwards'
min_max = 'min'
else:
concavity = 'downwards'
min_max = 'max'
return {'x': x, 'y': y, 'min_max': min_max, 'concavity': concavity}

def solver(equation):
if not isinstance(equation, Equation):
raise TypeError("Argument must be an Equation object")

# User Editable Region

output_string = f'\n{equation.type:-^24}'
output_string += f'\n\n{equation!s:^24}\n\n'

# User Editable Region

return output_string

lin_eq = LinearEquation(2, 3)
print(solver(lin_eq))

``````

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### Challenge Information:

Learn Interfaces by Building an Equation Solver - Step 53

i’ve managed to whip something together however it is still wrong this is just the idea i have in my head

Add on to `output_string` the same way you did in the previous step.

You are adding the word “Solutions”, which is a string.

I hope this helps!

yes that helped thank you, my friend