Answer:
[tex]x=-1;\ y=8\\x=5;\ y=2[/tex]
Step-by-step explanation:
You can make both equations equal and solve for the variable x, as you can see below:
[tex]-x+7=0.5(x-3)^2[/tex]
Keep on mind that:
[tex](a-b)^2=a^2-2ab+b^2[/tex]
Then:
[tex]-x+7=0.5(x-3)^2\\-x+7=0.5(x^2-2(x)(3)+3^2)\\-x+7=0.5x^{2}-3x+4.5\\0=0.5x^2-2x-2.5[/tex]
Apply the quadratic formula:
[tex]x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-(-2)+/-\sqrt{(-2)^2-4(0.5)(-2.5)}}{2(0.5)}\\x=-1\\x=5[/tex]
Substitute each value into one of the originl equations to find y, then:
[tex]y=-(-1)+7=8\\y=-5+7=2[/tex]
Answer:
The solutions are (-1,8) and (5,2).
Step-by-step explanation:
