Answer:
[tex]\implies \boxed{\red{\sf ( x +1)^2 = \dfrac{1}{4}}} [/tex]
Step-by-step explanation:
Given :-
- A equation is given to us
- The equation is 4x² + 8x + 3 = 0
And we need to write the equation by completing the square. Here's the step by step explanation .
Step 1: Make the coefficient of x² as 1 :-
[tex]\implies \dfrac{4x^2}{4} + \dfrac{8x}{4} + \dfrac{3 }{4}= 0 [/tex]
Step 2: Rewrite the equation :-
[tex]\implies x^2 + 2x +\dfrac{3}{4}= 0 [/tex]
Step 3: Add 1² to both sides :-
[tex]\implies x^2 + 2x + 1^2+\dfrac{3}{4}= 0 + 1^2 [/tex]
Step 4: Rewriting in whole square form:-
[tex]\implies ( x +1)^2 = 1 - \dfrac{3}{4} [/tex]
Step 5: Simplify the RHS :-
[tex]\implies ( x +1)^2 = \dfrac{4- 3}{4} [/tex]
Step 6: The required form of equⁿ :-
[tex]\implies ( x +1)^2 = \dfrac{1}{4} [/tex]
Hence the equation by rewriting it by completing the square is ( x + 1)² = 1/4 .
