11y+15=2y²
by factoring
pasagot with solution
nonsense - report
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11y+15=2y²
by factoring
pasagot with solution
nonsense - report
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To solve the equation 11y + 15 = 2y^2 by factoring, we want to rearrange the equation in quadratic form (ax^2 + bx + c = 0) and then factor it.
First, let’s bring all terms to one side to set the equation equal to zero:
2y^2 - 11y - 15 = 0
Now, we need to find two numbers that multiply to give -30 and add up to -11 (the coefficients of y^2 and y, respectively). These numbers are -15 and +2.
Next, we split the middle term (-11y) using these values:
2y^2 - 15y + 2y - 15 = 0
Now, let’s group the terms:
(2y^2 - 15y) + (2y - 15) = 0
Factor out the greatest common factor from each group:
Factor out the greatest common factor from each group:y(2y - 15) + 1(2y - 15) = 0
Now, we can factor out the common binomial, (2y - 15):
Now, we can factor out the common binomial, (2y - 15):(y + 1)(2y - 15) = 0
Now, to solve for y, we set each factor equal to zero and solve the resulting equations:
y + 1 = 0 --> y = -1
2y - 15 = 0 --> 2y = 15 --> y = 15/2 = 7.5
Therefore, the solutions to the equation 11y + 15 = 2y^2 by factoring are y = -1 and y = 7.5.