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Elementary Geometry for College St...
Solutions
Elementary Geometry for College St...
Determine the length
To find:
The length ‘
Solving an equation is to find the value of the unknown variables in the equation, such that the obtained value or values of the unknown should satisfy the equation from which it was derived. Such a value is said to be the solution for the equation. In general a quadratic equation has two solutions for the variable in the equation as the degree of the equation is two.
Calculation:
Given,
Apply the distributive property of multiplication over addition.
Add;
The above equation is in the standard form of a quadratic equation.
Now, we shall proceed with the factorization of the quadratic expression in the left of the equation.
First look for the common factor
But, here the
Thus, we have to factor the above equation by the reverse FOIL method.
First factorize the product of the coefficient of the first tern and the constant, such that the sum of the factors gives the coefficient of the middle term.
Thus, factorize
Now, split the middle term
Hence, the equation becomes,
Factor out the common factors form the first two terms and form the last two terms of the above expression
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