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X^{2} - 8x + 7 = 0<br> Solve by completing the square. Also can you include steps?

iren [92.7K]

Answer:

{1, 7}

Step-by-step explanation:

Start with x^2 - 8x + 7 = 0.

We want to modify the first two terms to resemble x^2 - ax + b - b, where a is the coefficient (here -8) of the x term and b is the square of half of a.

Here, a = -8. Half of that is -4. The square of -4 is 16, and this is the value of b.

Write out x^2 - 8x as x^2 - 8x + 16 - 16. This is the perfect square of -4, added to x^2 - 8x and then subtracted from the result

Then the original equation, x^2 - 8x + 7 = 0, can be rewritten as:

x^2 - 8x + 16 - 16 + 7 = 0, and then as (x - 4)^2 - 9, or (x - 4)^2 = 9.

We want to solve this result for x. To do this, take the square root of both sides:

x - 4 = ±√9, or x - 4 = ±3.

Adding 4 to both sides, we get:

x = 4 ± 3. Thus, the solutions are x = 4 + 3 = 7 and x = 4 - 3 = 1.

6 0

3 years ago

Read 2 more answers

the number of grams a woman should eat in a day to maintain her weight is proportional to her weight. a woman weighing 102 pound

vitfil [10]

Given:
grams of fat : 34 grams TO weight of woman : 102 pounds
grams of fat : ? TO weight of woman : 180 pounds

This is a proportion problem: 34 grams to 102 pounds.

We first have to convert a unit of measure to another to maintain uniformity of measure. let us convert pounds to grams:

102 pounds * 453.592 grams / pound = 46,266.384 grams
180 pounds * 453.592 grams / pound = 81,646.560 grams

34 grams to 46,266.384 grams = x grams to 81,646.560 grams

proportion: a:b = c:d where ad = bc

34 grams * 81,646.560 grams = x * 46,266.384 grams
2,775,983.04 grams² = x * 46,266.384 grams
2,775,983.04 grams² ÷ 46,266.384 grams = x
60 grams = x

A woman weighing 180 pounds should eat 60 grams of fat to maintain her weight.

7 0

3 years ago

You toss a pair of dice. (a determine the number of possible pairs of outcomes. you toss a pair of dice. (a determine the number

Eduardwww [97]

(a) $^{6}C_1 * ^{6}C_1 = 36$ different possibilities
(b) $P(even die 1): \frac{1}{2}$
$P(even die 2): \frac{1}{2}$

So, there is a 1 in 4 chance that both dice will show an even.

3 0

3 years ago

What is 89 divided by 6 in long division and how would u show ur work?

vovikov84 [41]

1 4 . 8 3333
6 8 9 50

14.8333

3 0

3 years ago

A parachute speed during a free fall reaches117 miles per hour What is the speed in feet per second At the speed how many feet w

qwelly [4]

Answer:

Speed is 171.6 ft/s and distance is 1716 feet

Step-by-step explanation:

Given that,

The speed of a parachute = 117 miles per hour.

1 mph = 1.47 ft/s

117 mph = 171.6 ft/s

We need to find the distance it travel during 10 s. We know that the distance covered is equal to the product of speed and time taken. So,

d = vt

$d=171.6\ ft/s\times 10\ s\\\\=1716\ \text{feet}$

Hence, this is the required solution.

3 0

2 years ago