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LekaFEV [45]
3 years ago
10

Solve x^2-8x=3 by completing the square. Which is the solution set of the equation

Mathematics
2 answers:
Ivenika [448]3 years ago
6 0

For this case we have the following expression:

x ^ 2-8x = 3

We must complete squares.

So:

We divide the middle term between two and we square it:

(\frac {-8} {2}) ^ 2, then:

x ^ 2-8x + (\frac {-8} {2}) ^ 2 = 3 + (\frac {-8} {2}) ^ 2\\x ^ 2-8x + (- 4) ^ 2 = 3 + 16

We have to, by definition:

(a-b) ^ 2 = a ^ 2-2ab + b ^ 2

Then, rewriting:

((x-4) ^ 2 = 19

To find the roots, we apply square root on both sides:

x-4 = \sqrt {19}

We have two solutions:

x_ {1} = \sqrt {19} +4\\x_ {2} = - \sqrt {19} +4

Answer:

((x-4) ^ 2 = 19\\x_ {1} = \sqrt {19} +4\\x_ {2} = - \sqrt {19} +4

kkurt [141]3 years ago
4 0

Answer:

{-0.36, 8.36) to the nearest hundredth.

Step-by-step explanation:

x^2 - 8x = 3

(x - 4)^2 - 16 = 3

(x - 4)^2 = 19

Taking square roots:

x - 4 = +/- √19

x =  4 +/- √19

x = {-0.36, 8.36} to nearest 1/100.

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