How do you solve 8x^2+4=-33x?

2 Answers
Don't Memorise
Apr 5, 2016

The solutions are:
x = color(blue)(-1/8

x= color(blue)( - 4

Explanation:

8x^2 + 4 = -33x

8x^2 + 4 + 33x = 0

8x^2 + 33x + 4 = 0

The equation is of the form color(blue)(ax^2+bx+c=0 where:

a=8, b=33, c=4

The Discriminant is given by:

Delta=b^2-4*a*c

= (33)^2-(4* 8 * 4)

= 1089 -128= 961

The solutions are found using the formula
x=(-b+-sqrtDelta)/(2*a)

=(-33+-sqrt961)/(2*8)

=(-33+-31)/(16)

x =(-33+31)/(16) = -2/16 = color(blue)(-1/8

x =(-33-31)/(16) = -64/16 = color(blue)( - 4

Nghi N.
Apr 6, 2016

1/8 and 4

Explanation:

y = 8x^2 + 33x + 4 = 0
Use the new Transforming Method (Google and Yahoo Search).
Transformed equation: y' = x^2 + 33x + 32.
Since a - b + c = 0, use shortcut. Two real roots of y' are: -1 and (-c/a = -32).
Back to y, divide these real roots by (a = 8) to get the 2 real roots of y --> : x1 = -1/8 and x2 = -32/8 = -4.

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