SaiBook.us Algebra

Example

Title: Solve the equation

Grade: 9-a Lesson: S1-L2

Explanation: The best way to understand algebra is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

1. Solve \$sqrt(a^2 - 45) = 6 \$.

Step 1a

Given equation is that, \$sqrt(a^2 - 45) = 6 \$.

Perform squaring on both sides of the equation.

$1a$

Explanation: Given equation is that, \$sqrt(a^2 - 45) = 6 \$.

Do squaring on both sides of the equations, \$sqrt(a^2 - 45) = 6 \$.

⇒ \$(sqrt(a^2 - 45))^2 = 6^2\$.

Step 1b

Evaluate the exponents.

$1b$

Explanation: Evaluate the exponents

⇒ \$(sqrt(a^2 - 45))^2 = 6^2\$
⇒ \$(a^2 - 45) = 6^2\$
⇒ \$(a^2 - 45) = 36\$

Step 1c

Now solve for 'a'

$1c$

Explanation: Now solve for 'a'

i.e, move constant terms to one side of the equation.

⇒ \$(a^2 - 45) = 26\$
⇒ \$a^2 = 26 + 45\$
⇒ \$a^2 = 81\$

Apply square root on both sides of the equation.
⇒ \$sqrta^2 = sqrt81\$
⇒ \$a = 9\$