(x%2B6)%3D0-in-standard-form.jpeg "(2x-1)(x+6)=0 In Standard Form")
Solving Quadratic Equations: (2x-1)(x+6) = 0
This equation is already in a factored form, making it easier to solve. Let's break down the steps:
Understanding the Zero Product Property
The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero.
In our case, we have two factors: (2x-1) and (x+6). To satisfy the Zero Product Property, one or both of these factors must equal zero.
Solving for x
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Set each factor equal to zero:
- 2x - 1 = 0
- x + 6 = 0
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Solve each equation:
- 2x - 1 = 0
- Add 1 to both sides: 2x = 1
- Divide both sides by 2: x = 1/2
- x + 6 = 0
- Subtract 6 from both sides: x = -6
- 2x - 1 = 0
The Solutions
Therefore, the solutions to the equation (2x-1)(x+6) = 0 are x = 1/2 and x = -6.
Standard Form
While the factored form is helpful for solving, we can also express the equation in standard form, which is ax² + bx + c = 0.
To do this, we simply expand the factored form:
(2x-1)(x+6) = 0 2x² + 12x - x - 6 = 0 2x² + 11x - 6 = 0
This is the standard form of the quadratic equation.