Question

What is the intermediate step in the form (x + a)2 = b as a result of completing the

square for the following equation?
x^2 – 3x = 7x - 30

Answer 1

( x - 5 )² = 75

Explanation:

We need to convert the given equation in

• (x + a)² = b form .

So for that , let's complete the square of the given quadratic equation .

=> x² - 3x = 7x - 30

=> x² -3x - 7x + 30 = 0

=> x² - 10x + 30 = 0

=> x² - 2(5)x + 30 = 0

=> x² - 2(5)x +5² -30 = 5²

=> x² - 2(5)x + 5² = 25 +30

=> ( x - 5 )² = 75

Hence wrt the given form , the value of a is (-5) and b is 75 .

Hence the required answer is ( x - 5)² = 75