Prof. Martin tried to solve the quadratic equation y = 8x2 − 5x − 3 by completing the square, but she made a mistake.

In which line of her work shown below did she make the mistake?
8x2 − 5x − 3 = 0
[Line 1] ⇒ 8x2 − 5x = 3
[Line 2] ⇒ x2 − 0.625x = 0.375
[Line 3] ⇒ x2 − 0.625x + 0.09765625 = -1.25 + 0.09765625
[Line 4] ⇒ (x − 0.3125)2 = -1.25 + 0.09765625
[Line 5] ⇒ (x − 0.3125)2 = 0.47265625
[Line 6] ⇒ x − 0.3125 = ±√(0.47265625)
[Line 7] ⇒ x = ±√(0.47265625) − 0.3125
[Line 8] ⇒ x = -0.375 or 1.000, rounded to 3 decimal places

Line 5

Line 4

Line 6

Line 7

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9

one way is to plot 2 points and connect them which is what the answer choices seem to be doing

it seems to be using the y intercept and the slope

y=mx+b, m=slope, b=y-intercept (where the line hits the y axis)

slope=rise/run

y-intercept is where the line croses the y axis which is the y value where x=0

you seem to have given the wrong slope (you didn't put a number in front of te x, it should be 2/3 or 3/2 looking at the answer options)

y=? x-1

m=? because of your fault

b=-1

so it has a slope of ? and y intercept of -1, meaning it pases through (0,-1)

so draw point (0,-1) (so answer is one of the first 2 option)

if slope is 2/3, then go up 2 and right 3 then draw line through those 2 points

if slope is 3/2, then go up 3 and right 2 then draw line through those 2 points