(x%2B4)%3D0-in-standard-form-brainly.jpeg "(x+3)(x+4)=0 In Standard Form Brainly")
Solving (x+3)(x+4) = 0 and Putting it in Standard Form
This equation is already in a factored form, making it easy to solve for the values of x. Let's break down the steps:
Understanding the Zero Product Property
The equation (x+3)(x+4) = 0 utilizes 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.
Solving for x
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Set each factor equal to zero:
- x + 3 = 0
- x + 4 = 0
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Solve for x in each equation:
- x = -3
- x = -4
Therefore, the solutions to the equation (x+3)(x+4) = 0 are x = -3 and x = -4.
Standard Form
The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants. To put the equation in standard form, we need to expand the factored form:
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Expand the equation: (x+3)(x+4) = 0 x² + 4x + 3x + 12 = 0
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Combine like terms: x² + 7x + 12 = 0
Therefore, the standard form of the equation (x+3)(x+4) = 0 is x² + 7x + 12 = 0.
Key Takeaways
- The Zero Product Property is a valuable tool for solving equations in factored form.
- Standard form makes it easier to identify the coefficients and constant term of a quadratic equation.
- Remember that the solutions to the equation (x+3)(x+4) = 0 are the values of x that make the equation true, which are x = -3 and x = -4.