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zvonat [6]
2 years ago
7

6x squared plus 12x plus 13 equals 2x squared plus 4

Mathematics
1 answer:
Andrews [41]2 years ago
6 0
12x^2+12x+3=2x^2+4\\\\12x^2-2x^2+12x+3-4=0\\\\10x^2+12x-1=0\\\\a=10;\ b=12;\ c=-1\\\\\Delta=12^2-4\cdot10\cdot(-1)=144+40=184\\\\x_1=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{184}=\sqrt{4\cdot46}=2\sqrt{46}\\\\x_1=\frac{-12-2\sqrt{46}}{2\cdot10}=\frac{-6-\sqrt{46}}{10};\ x_2=\frac{-12+2\sqrt{46}}{2\cdot10}=\frac{-6+\sqrt{46}}{10}
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Either would work, but substitution looks a bit easier.

The graph for these two is shown below.


I just put the equations in just as they are written. They did not have to be changed in any way. DESMOS is a wonderful program. Very powerful.


The blue line is 2x + y = - 6

The red line is y = x + 3


The best way to solve this other than a graph is to use substitution. Put the red graph into the blue one.

2x + y = - 6

2x +(x + 3) = - 6

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x = -9/3

x = -3


Now go back and solve for y

y = x + 3

y = -3 + 3

y = 0


Answer

The solution point is (-3,0) just what the graph shows.

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