How do you solve #2a ^ { 2} + 24a = - 92#?

1 Answer
tcw1
Jul 31, 2017

No real number solution.

Using imaginary numbers: #x=-6 \pm i sqrt (10)#

Explanation:

#2a^2+24a=-92#
Add 92 to each side
#2a^2+24a+92=0#
Divide both sides by 2
#a^2+12a+46=0#
Apply the quadratic formula, #x=(-b \pm sqrt(b^2-4ac))/(2a)#, where a=1, b=12, and c=46
#x=(-12 \pm sqrt(12^2-4(1)(46)))/(2(1))#
#x=(-12 \pm sqrt(144-184))/(2)#
#x=(-12 \pm sqrt(-40))/(2)#
Because this requires a square root of a negative number, we see that there is no real number solution for this equation.
Using imaginary numbers:
#x=-6 \pm sqrt (-10)#
#x=-6 \pm i sqrt (10)#

Looking at the graph:Google the equation never reaches -92, meaning there is no solution.

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