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Solving three equations for x ​

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I managed to get a start on the first one, but now I'm stuck. I have no clue how to do the other two.

a.

y - 3x = 2z^2 + 8

y - 3x = 2(5x-3)^2 + 8

y - 3x =  2(25x^2 - 30x + 9) + 8

y - 3x =  50x^2 - 60x + 26

50x^2 - 60x + 26 = y - 3x

50x^2 - 57x + 26 = y

?

b. ?

c. ?

Jan 3, 2021

#1
+112816
+1

I assume you are being asked to make x the subject.

I'll start half way through your working.

$$y - 3x = 50x^2 - 60x + 26\\ y = 50x^2 - 57x + 26\\ 2y-52 = 100x^2 - 114x \\ \frac{2y-52}{100} = x^2 - 1.14x \\ \text{Complete the square}\\ \frac{2y-52}{100} +(0.57)^2= x^2 - 1.14x+(0.57)^2 \\ \frac{2y-52}{100} +0.3249= (x-0.57)^2 \\ \frac{2y-52+32.49}{100} = (x-0.57)^2 \\ \frac{2y-19.51}{100} = (x-0.57)^2 \\ \pm\frac{\sqrt{2y-19.51}}{10} = (x-0.57) \\ x=0.57\pm\frac{\sqrt{2y-19.51}}{10} \\ x=\frac{5.7\pm\sqrt{2y-19.51}}{10} \\$$

You will need to check for careless mistakes.

Jan 3, 2021
#2
+112816
0

The second one is easy.  The last one is not so bad either.

Jan 3, 2021