To solve the equation m² + 14m + 49, we can begin by trying to factor it.
Looking at the expression, we notice that the first and last terms are perfect squares (m² and 49, respectively), and the middle term (14m) is twice the product of the square roots of the first and last terms.
Based on this observation, we can rewrite the equation as:
(m + 7)² = 0
Applying the zero product property, we know that the equation will be true when (m + 7) equals zero.
Setting m + 7 = 0 and solving for m, we have:
m = -7
Therefore, the solution to the equation m² + 14m + 49 = 0 is m = -7.
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Step-by-step explanation:
To solve the equation m² + 14m + 49, we can begin by trying to factor it.
Looking at the expression, we notice that the first and last terms are perfect squares (m² and 49, respectively), and the middle term (14m) is twice the product of the square roots of the first and last terms.
Based on this observation, we can rewrite the equation as:
(m + 7)² = 0
Applying the zero product property, we know that the equation will be true when (m + 7) equals zero.
Setting m + 7 = 0 and solving for m, we have:
m = -7
Therefore, the solution to the equation m² + 14m + 49 = 0 is m = -7.