Need help solving:  x(2x+7)=0  & 9x squared + 12x +14 (the answer is a fraction)I do not understand factoring the quadratic equation when the answer is a fraction. Actually, I do understand...

Need help solving:  x(2x+7)=0  & 9x squared + 12x +14 (the answer is a fraction)

I do not understand factoring the quadratic equation when the answer is a fraction. Actually, I do understand how to factor these types of equations at all.

Asked on by estickney

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll solve the first equation:

x(2x+7) = 0

The product is cancelling if one of the factors is cancelling.

We'll cancel out the first factor, x:

x = 0

We'll cancel out the next factor, x:

2x+  7 = 0

2x = -7 =>> x = -7/2

We'll solve the second equation

9x^2 + 12x + 14 = 0

We'll apply quadratic formula to determine it's roots::

x1 = [-b+sqrt(b^2-4ac)]/2a

We'll identify he coefficients a,b,c.

a = 9, b = 12 and c = 14

x1 = [-12+sqrt(144 - 504)]/18

x1 = [-12+sqrt(-360)]/18

x1 = (-12+6i*sqrt10)/18

We'll divide by 6:

x1 = (-2+i*sqrt10)/3

x2 = (-2-i*sqrt10)/3

The real roots of the 1st equation are x = 0 and x = -7/2 and the roots of the 2nd equation are complex number and they are x1 = (-2+i*sqrt10)/3 and x2 = (-2-i*sqrt10)/3.

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