Solve for y.
\[ y^2 + 14y + 49 = 0 \]
Answer (2)
y 2 + 14 y + 49 = 0 ( ∗ ) y 2 + 2 ⋅ y ⋅ 7 + 7 2 = 0 ( y + 7 ) 2 = 0 ⟺ y + 7 = 0 → y = − 7 − − − − − − − − − − − − − − − − − − − − − − − ( ∗ ) ( a + b ) 2 = a 2 + 2 ab + b 2
The solution to the quadratic equation y 2 + 14 y + 49 = 0 is y = − 7 . This is found by recognizing the equation is a perfect square and factoring it. We verify by substituting back into the original equation to confirm it equals zero.
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