Find the roots of the quadratic equation x2 – 8x = 9 by completing the square. show your work.

The answer is -1 or 9

The quadratic equation is ax² + bx + c  = 0. But, by completing the square we turn it into: a(x + d)² + e = 0, where:

d = b/2a

e = c - b²/4a

Our quadratic equation is x² - 8x = 9, which is after rearrangement:

x² - 8x - 9 = 0

So, a = 1, b = -8, c = -9

Let's first calculate d and e:

d = b/2a = -8/(2 * 1) = -8/2 = -4

e = c - b²/4a = -9 - (-8)²/(4 * 1) = -9 - 64/4 = -9 - 16 = -25

By completing the square we have:

a(x + d)² + e = 0

1(x + (-4))² + (-25) = 0

(x - 4)² - 25 = 0

(x - 4)² = 25

⇒ x - 4 = √25

Since √25 can be either -5  or +5 , then:

x - 4 = -5             or           x - 4 = 5

x = -5 + 4            or           x = 5 + 4

x = -1                   or           x = 9

Step-by-step explanation:

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!

income. 10x+1300

expenses 3x+(1800+1500)

expenses 3x+3300

to break even:

income = expense,

10x + 1300 = 3x + 3300,

solve for x.

step-by-step explanation:

mark brainliest