Determine the length by solving either the equation or the equivalent equation .
The length ‘’ by solving the equation .
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.
Apply the distributive property of multiplication over addition.
Add; on both side,
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 of the terms , and .
But, here the is .
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 as so that the sum of the factors gives .
Now, split the middle term as .
Hence, the equation becomes,
Factor out the common factors form the first two terms and form the last two terms of the above expression
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Single Variable Calculus: Early Transcendentals, Volume I
Calculus: Early Transcendentals
Calculus (MindTap Course List)
Single Variable Calculus
Finite Mathematics and Applied Calculus (MindTap Course List)
Calculus: Early Transcendental Functions
Statistics for The Behavioral Sciences (MindTap Course List)
Mathematical Applications for the Management, Life, and Social Sciences
Precalculus: Mathematics for Calculus (Standalone Book)
Essentials Of Statistics
Elementary Technical Mathematics
Understanding Basic Statistics
Calculus: An Applied Approach (MindTap Course List)
Mathematical Excursions (MindTap Course List)
Probability and Statistics for Engineering and the Sciences
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Elements Of Modern Algebra
Trigonometry (MindTap Course List)
Single Variable Calculus: Early Transcendentals
Calculus of a Single Variable
Contemporary Mathematics for Business & Consumers
Finite Mathematics for the Managerial, Life, and Social Sciences
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Study Guide for Stewart's Multivariable Calculus, 8th
Calculus: Early Transcendental Functions (MindTap Course List)