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10y^2+45y-25?

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2 Answers

The first step is to set the equation to zero.

10y^2 + 45y - 25 = 0

Next you extract the common factors.

10y^2 + 45y - 25 = 5(2y^2 + 9y - 5)

2y^2 + 9y - 5 = 0

a = 2, b = 9, c = -5

Discriminant: d = b^2 - 4*a*c = 9^2 - 4*2*(-5) = 81 + 40 = 121

Quadratic Formula: y = [-b +/- sqrt(d)]/2*a

In this case

y = [-9 +/- sqrt(121)]/2*2 = (-9 +/- 11)/4 = -5 or 1/2

y = -5 --> y + 5 = 0

y = 1/2 --> y - 1/2 = 2y - 1 = 0

Hi Courtnee!

Look at the last term "25" -- what factors are available? 5x5 ... (y+5)(y-5) = y^2 + 5y - 5y - 25 ... not quite

The -25 looks good, but the middle terms for y cancel out -- we need 45y ...

If we can get +50y instead of just +5y .............\/...\/

Look at the 1st term "10" -- factors? 10x1 ... (y+5)(10y-5) = 10y^2 + 50y - 5y -25

Summary: set usable factors from last term, then "tweak" factors of 1st term to get middle term :)