(2x+1)(x-7)=0

Jasonbradley

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Jun 16, 2024

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Solving the Equation: (2x+1)(x-7) = 0

This equation represents a quadratic equation in factored form. To solve for x, we can utilize 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.

Applying the Zero Product Property

1. Set each factor equal to zero:

   • 2x + 1 = 0
   • x - 7 = 0

2. Solve for x in each equation:

   • For 2x + 1 = 0:
     • 2x = -1
     • x = -1/2
   • For x - 7 = 0:
     • x = 7

Solutions

Therefore, the solutions to the equation (2x + 1)(x - 7) = 0 are:

• x = -1/2
• x = 7

These solutions represent the x-intercepts of the parabola represented by the equation.