What is x if #-4x+9/x=-30#?

2 Answers
Nghi N.
Jul 31, 2016

#(15 +- 3sqrt29)/4#

Explanation:

Multiply both sides of the equation by x -->
-4x^2 + 9 = - 30x
y = - 4x^2 + 30x + 9 = 0
Solve this equation by the new quadratic formula in graphic form (Socratic Search).
#D = b^2 = b^2 - 4ac = 900 + 144 = 1044 = 36(29)#--> #d = +- 6sqrt29#
There are 2 real roots:
#x = -b/(2a) +- d/(2a) = -30/-8 +- (6sqrt29)/8 = (15 +- 3sqrt29)/4#

EZ as pi
Jul 31, 2016

#x = 7.7889 or x = -0.2889#

Explanation:

The fact that #x# is in the denominator already means that we assume it is not equal to 0.

Multiply all the terms by #x# to get rid of the fraction.

#color(red)(x xx) -4x +(color(red)(x xx)9)/x=color(red)(x xx)-30#

#-4x^2 + 9 =-30x" re-arrange and make" =0#

#0 = 4x^2 -30x-9" does not factorise"#

Use the formula: #a = 4, b= -30, c= -9#

#x = (-b+-sqrt(b^2-4ac))/(2a)#

#x = ((-(-30)+-sqrt((-30)^2-4(4)(-9))))/(2(4)#

#x = (30+-sqrt(900+144))/(8))#

#x = (30+-sqrt(1044))/(8)#

#x = 7.7889 or x = -0.2889#

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