(x-7)%3D0-in-standard-form.jpeg "(x+7)(x-7)=0 In Standard Form")
Solving the Equation (x+7)(x-7) = 0
The equation (x+7)(x-7) = 0 is a quadratic equation in factored form. This form makes it easy to solve for the values of x.
Understanding Factored Form
In factored form, a quadratic equation is expressed as the product of two linear factors. Each factor represents a linear expression that can be set equal to zero. This is based on the Zero Product Property: If the product of two or more factors is zero, then at least one of the factors must be equal to zero.
Solving the Equation
-
Set each factor equal to zero:
- (x+7) = 0
- (x-7) = 0
-
Solve for x in each equation:
- x = -7
- x = 7
Therefore, the solutions to the equation (x+7)(x-7) = 0 are x = -7 and x = 7.
Standard Form
The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants. To rewrite the equation in standard form, we can expand the factored form:
(x+7)(x-7) = x² - 7x + 7x - 49 = x² - 49
Therefore, the standard form of the equation is x² - 49 = 0.
Conclusion
By understanding the Zero Product Property and factoring, we can easily solve quadratic equations. The factored form provides a direct path to the solutions, while the standard form offers a more general representation of the equation.