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.
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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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