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5. Solving Quadratics
Problem:
Solve the quadratic equation:
x² - 5x + 6 = 0
6. Simplifying Expressions
Problem:
Simplify the expression:
(2x + 3) - 4(2x - 1)
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Reading the question
Identifying key values and variables
Explanation:
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Step1: Identify the
quadratic equation
x² - 5x + 6 = 0
Step2: Factor the quadratic
Step3: Apply the zero
product property
x - 2 = 0 or x - 3 = 0
Step4: Solve for the
variable x
x = 2, x = 3
Answer:
x = 2, 3
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Factoring Quadratic Equations
The Breaker
"You tried to solve it... should've factored first."
x²+5x+6=0
FIND TWO
NUMBERS THAT:
MULTIPLY TO 6
(+2)(+3)
ADD TO 5
(constant term c)
(b coefficient)
=0
Shatter complex ax²+bx+c=0 equations by
factoring them into pieces! Use the Zero Product
Property to reveal the hidden roots with ease.
Key Points
Break down ax²+bx+c into linear binomial
factors.
Apply the Zero Product Property to each factor.
Solve for x to find the roots or x-intercepts.
Quick Example
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Substitution Method
Alias Agent
"Assume the identity to solve the case."
y = 2x
x + y = 6
Solve systems of linear equations, one example and
other equation, reducing the system to a single-variable
equation.
Key Points
Isolate one variable (x or y) in the simplest
equation.
Substitute that expression into the second
equation.
Solve the resulting equation and back-
substitute the value.
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Order of Operations
Rank Marshal
"Follow the chain of command."
ORDER OF OPERATIONS HIERARCHY
1. PARENTHESES
2. EXPONENTS
3. MULTIPLICATION & DIVISION
4. ADDITION & SUBTRACTION
The Order of Operations Hierarchy
P -> E -> MD -> AS.
Key Points
Evaluate Parentheses and Exponents first.
Process Multiplication and Division from left to
right.
Complete Addition and Subtraction as the final
step.
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Short
Solving for
(a ≠ 0) to
Maintain
both sides
Undo addition
with division
Target the
variable