Solve for \( x \):
\[ 6x^2 + 12x + 13 = 2x^2 + 4 \]
Answer (2)
12 x 2 + 12 x + 3 = 2 x 2 + 4 12 x 2 − 2 x 2 + 12 x + 3 − 4 = 0 10 x 2 + 12 x − 1 = 0 a = 10 ; b = 12 ; c = − 1 Δ = 1 2 2 − 4 ⋅ 10 ⋅ ( − 1 ) = 144 + 40 = 184 x 1 = 2 a − b − Δ ; x 2 = 2 a − b + Δ Δ = 184 = 4 ⋅ 46 = 2 46 x 1 = 2 ⋅ 10 − 12 − 2 46 = 10 − 6 − 46 ; x 2 = 2 ⋅ 10 − 12 + 2 46 = 10 − 6 + 46
To solve the equation, we first rearranged it to form a quadratic equation, 4 x 2 + 12 x + 9 = 0 . Using the quadratic formula, we found that the only solution is x = − 2 3 . The discriminant being zero indicates one real solution exists.
;
