Find the roots of the equation 5x2 - 6x - 2 = 0 by the method of completing the square
Solution:
Let us solve the equation using the method of completing the square
Given, 5x2 - 6x - 2 = 0
Step1: Rewrite the equation in the form of ax2 + bx = c
⇒ 5x2 - 6x = 2
Step 2: Divide the coefficient of x2 by the equation
⇒ x2 - 6/5x = 2/5
Step 3: Divide the coefficient of x by 2 and then add the square of x/ 2 to both the sides of the equation.
⇒ x2 - 6/5x + (⅗)2 = ⅖ + (⅗)2
Step 4: Solve the equation using the algebraic identity (a - b)2 = a2 - 2ab + b2
⇒ (x - ⅗ )2 = 19/25
Step 5: Taking square root on both sides.
⇒ x - ⅗ = 19/25
Step 6: Add 19/25 to both sides.
⇒ x = ⅗ ± 19/25
⇒ x = (3 + √19) / 5 and (3 - √19) / 5
The solution of the equation 5x2 - 6x - 2 = 0 is (3 + √19) / 5 and (3 - √19) / 5 using the method of completing the square
☛ Check: NCERT Solutions for Class 10 Maths Chapter 4
Find the roots of the equation 5x2 - 6x - 2 = 0 by the method of completing the square
Summary:
The solution for the equation 5x2 - 6x - 2 = 0, by the method of completing the square is (3 + √19) / 5 and (3 - √19) / 5
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