(2x-1)(x+4)=0

Jasonbradley

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Jun 16, 2024

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Solving the Equation (2x-1)(x+4) = 0

This equation is a simple quadratic equation in factored form. To solve for x, we can use the Zero Product Property. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Here's how to solve it:

1. Set each factor equal to zero:

   • 2x - 1 = 0
   • x + 4 = 0

2. Solve each equation for x:

   • 2x = 1
   • x = 1/2
   • x = -4

Therefore, the solutions to the equation (2x-1)(x+4) = 0 are x = 1/2 and x = -4.

Explanation:

The Zero Product Property allows us to separate a single equation into two simpler equations. By setting each factor equal to zero, we can find the values of x that make the original equation true.

In this case, the original equation is true when either:

• 2x - 1 = 0 (which is true when x = 1/2)
• x + 4 = 0 (which is true when x = -4)

Important Note: This method of solving quadratic equations works only when the equation is in factored form. If the equation is not factored, you can use other methods like the quadratic formula or completing the square to solve it.