Math Problem Statement
Solve the equation by factoring. (Enter your answers as a comma-separated list.) −4x2 − 6x + 4 = 0 slove for x
Solution
The given quadratic equation is:
Step 1: Simplify the equation
We can start by dividing the entire equation by to simplify it:
Step 2: Factor the quadratic equation
We are looking for two numbers that multiply to and add up to .
The numbers and satisfy these conditions, because:
Now, we can rewrite the middle term and factor by grouping:
Group the terms:
Factor each group:
Factor out the common binomial factor :
Step 3: Solve for
Set each factor equal to 0:
Final Answer:
The solutions are:
Would you like further details or have any questions?
Here are 5 related questions:
- How can you check if your factored solution is correct?
- What are other methods to solve a quadratic equation?
- What is the quadratic formula, and how does it apply here?
- How do you know when a quadratic equation cannot be factored?
- What are the differences between factoring and completing the square?
Tip: Always simplify the quadratic equation by removing common factors before factoring.
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Math Problem Analysis
Mathematical Concepts
Algebra
Factoring
Quadratic Equations
Formulas
Quadratic equation formula: ax^2 + bx + c = 0
Factoring by grouping
Theorems
Zero Product Property
Suitable Grade Level
Grades 9-11