# Solve equation!!!!!!!!!!!!!!!!!!!!!!!!!

+1 vote
x^2-3x-18=0 and x^2-2x-8=0?

+1 vote

The equation x^2 - 3*x - 18 = 0 is already in a*x^2+b*x+c=0 form.
As the value is already arranged in a*x^2+b*x+c=0 form, we get the value of a = 1, b = -3, c = -18.

Remember the formula,
x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a)
Since a = 1, b = -3 and c = -18,
we just need to subtitute the value of a,b and c in the abc formula.
Which produce x1 = (-(-3) + sqrt( (-3)^2 - 4 * (1)*(-18)))/(2*1) and x2 = (-(-3) - sqrt( (-3)^2 - 4 * (1)*(-18)))/(2*1)
Which is the same as x1 = ( 3 + sqrt( 9+72))/(2) and x2 = ( 3 - sqrt( 9+72))/(2)
Which make x1 = ( 3 + sqrt( 81))/(2) and x2 = ( 3 - sqrt( 81))/(2)
We got x1 = ( 3 + 9 )/(2) and x2 = ( 3 - 9 )/(2)
The answers are x1 = 6 and x2 = -3

x² - 2x - 8 = 0
=>x² + 2x - 4x - 8 = 0 [splitting the middle term]
=>x(x + 2) - 4(x + 2) = 0
=>(x + 2)(x - 4) = 0
because the terms in multiplication result to zero, either of the terms is equal to zero.
so keeping both the factors equal to 0
>> x + 2 = 0
=> x = -2
>> x - 4 = 0
=> x = 4
the answer finally is x = -2 , 4

The equation is x2 - 3x - 18 = 0.

By factoring by grouping.

x2 - 6x + 3x - 18 = 0

x(x - 6) + 3(x - 6) = 0

Factor : (x - 6)(x + 3) = 0

Apply zero product property.

x - 6 = 0  and  x + 3 = 0

x = 6  and  x = - 3

The solutions are x = 6 and x = - 3.

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The equation is x2 - 2x - 8 = 0.

By factoring by grouping.

x2 - 4x + 2x - 8 = 0

x(x - 4) + 2(x - 4) = 0

Factor : (x - 4)(x + 2) = 0

Apply zero product property.

x - 4 = 0  and  x + 2 = 0

x = 4  and  x = - 2

The solutions are x = 4 and x = - 2.