Question 30991
Your eqn is
x² - 7x + 5 = 0
When you square a term like (x+a) you get,
(x+a)² = x² + 2ax + a²
Look at the coefficient of the x-term. It is 2a. Compare that with the coefficient of the x-term in your own eqn. You have: -7.
So equate the coefficient values.
2a = -7
a = -7/2
========
(x+a)² = (x-7/2)² = x² -7x + 7²/2² = x² -7x + 49/4
You've got an extra constant term, 49/4, so add and subtract this to keep your original eqn unaltered.
x² - 7x + 5 = 0 becomes,
x² -7x + 49/4 - 49/4 + 5 = 0
(x-7/2)² -49/4 + 20/4 = 0
(x-7/2)² = 49/4 - 20/4 = 29/4
(x-7/2)² = 29/4
Take the square root of both sides,
(x-7/2) = √29/2
x = 7/2 +/- √29/2
===============
In decimals, that becomes
x = 3.5 +/- 2.6926
x = 6.1926, x = 0.8074
======================