5x2
-2 -6x =0. Find the roots by completeing the square.
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Given equation:
5x² - 2 - 6x = 0
- Make the coefficient of x² as 1.
(5x² - 6x - 2)/5 = x² - (6/5)x - (2/5) = 0
- Multiply the coefficient of x by 1/2. Add and subtract the square of the obtained number from the equation.
Coefficient of x = 6/5.
Multiply it by 1/2: 6/5 × 1/2 = 3/5
Add and subtract the square of this number: x² - (6/5)x + (3/5)² - (3/5)² - (2/5) = 0
- Solve the first three terms as the identity: a² - 2ab + b² = (a + b)²
x² - (6/5)x + (3/5)² - (3/5)² - (2/5) = 0
=> (x - 3/5)² - (9/25) - (2/5) = 0
- Take the other two left terms to LHS and solve.
=> (x - 3/5)² = (9/25) + (2/5)
=> (x - 3/5)² = (9 + 10)/25 [Take LCM]
=> x - 3/5 = +(_/19)/5 , -(_/19)/5
=> x = (3 + _/19)/5 , (3 - _/19)/5
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