(x%2B4)%3D0-foil-method.jpeg "(x+3)(x+4)=0 Foil Method")
Solving Quadratic Equations Using the FOIL Method: (x+3)(x+4) = 0
The FOIL method is a mnemonic acronym for the steps used to multiply two binomials. It stands for First, Outer, Inner, Last. This method helps us to systematically expand the product of two binomials and solve quadratic equations.
Let's break down how to solve the equation (x+3)(x+4) = 0 using the FOIL method:
1. Expanding the Equation
Step 1: Multiply the First terms of each binomial.
- (x) * (x) = x²
Step 2: Multiply the Outer terms of the binomials.
- (x) * (4) = 4x
Step 3: Multiply the Inner terms of the binomials.
- (3) * (x) = 3x
Step 4: Multiply the Last terms of each binomial.
- (3) * (4) = 12
Now, combine all the terms:
- x² + 4x + 3x + 12 = 0
Step 5: Simplify the equation by combining like terms.
- x² + 7x + 12 = 0
2. Solving the Quadratic Equation
The equation x² + 7x + 12 = 0 is now in standard quadratic form (ax² + bx + c = 0). We can solve this equation by factoring or by using the quadratic formula.
Factoring Method:
- Find two numbers that add up to 7 (the coefficient of the x term) and multiply to 12 (the constant term).
- These numbers are 3 and 4.
- Rewrite the equation as: (x + 3)(x + 4) = 0
Zero Product Property:
- The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero.
- Therefore, either (x + 3) = 0 or (x + 4) = 0
Solving for x:
- x + 3 = 0 => x = -3
- x + 4 = 0 => x = -4
Conclusion
By using the FOIL method to expand the equation (x+3)(x+4) = 0, we were able to solve the quadratic equation and find the solutions: x = -3 and x = -4.