how can you solve quadratic equation in one variable using extracting the square roots?
Answers
Given : quadratic equation in one variable
To Find : How to solve using extracting the square roots
or Complete the square roots
Solution:
ax² + bx+ c = 0
(x + y)² = (x² + 2xy + y²)
(x - y)² = ( x² - 2xy + y²)
ax² + bx+ c = 0
Divide both sided by a
=> x² + (b/a)x + c = 0
=> x² + 2. x (b/2a) + c = 0
Add and subtract (b/2a)²
=> x² + 2x. (b/2a) + (b/2a)² - (b/2a)² + c = 0
=> (x + b/2a)² = -c + (b/2a)²
=> x + b/2a = ± √ (-c + (b/2a)²)
=> x = - b/2a ± √ (c + (b/2a)²)
=> x = { - b ± √ (b² - 4ac ) }/2a
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