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Mathematics
Elena Franco
16 July, 16:03
Solve for y.
2y^2+5y+63 = (y+7) ^2
+3
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1
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Piper Sanchez
16 July, 16:16
0
Answer: y = 2 or 7
Step-by-step explanation:Copy and open the bracket
2y² + 5y + 63 = (y + 7) ²
expand the right hand expression (y + 7) ², which now becomes
y² + 14y + 49, now equate the 2 together and arrange it into a quadratic structure
2y² + 5y + 63 = y² + 14y + 49
2y² - y² + 5y - 14y + 63 - 49 = 0
y² - 9y + 14 = 0
Now, factorize the expression using grouping or any method
y² - 7y - 2y + 14 = 0, considering two factors, when multiplied together gives + 14, and when added together gives - 9
Considering the common factors, it now becomes
y (y - 7) - 2 (y - 7) = 0
(y - 2) (y - 7) = 0
To find the root of y,
when y - 7 = 0
y = 7, and when y - 2 = 0, y = 2
Therefore, the solution of the equation is
y = 2, or 7.
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