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frosja888 [35]
3 years ago
12

Find the sum of all solutions to the equation $3x(x+4) = 66$.

Mathematics
2 answers:
Solnce55 [7]3 years ago
6 0
Https://photomath.net/s/o2P0wN
vovikov84 [41]3 years ago
5 0

Answer:

the solutions are:

x_{1}=-2+\sqrt{26}

x_{2}=-2-\sqrt{26}

and the sum of solutions is:

-4

Step-by-step explanation:

the expression is:

3x(x+4)=66\\

doing the multiplication

3x^2+12x=66\\\\3x^2+12x-66=0

dividing everything by 3:

x^2+4x-22=0

we use the quadratic formula to find the solutions:

in this case since we have an equation in the form

ax^2+bx+c=0

where

a=1\\b=4\\c=-22

the quadratic formula is:

x=\frac{-b+-\sqrt{b^2-4ac} }{2a} \\\\x=\frac{-4+-\sqrt{4^2-4*1*(-22))=} }{2}\\ x=\frac{-4+-\sqrt{16+88} }{2} \\ x=\frac{-4+-\sqrt{104} }{2} \\\\ x=\frac{-4+-2\sqrt{26} }{2} \\\\\\x=-4+-\sqrt{26}

from this, using the + sign we find the first solution:

x_{1}=-2+\sqrt{26}

and the second solution:

x_{2}=-2-\sqrt{26}

the sum of the solutions is:

x_{1}+x_{2}=-2+\sqrt{26}-2-\sqrt{26}\\  x_{1}+x_{2}=-4

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