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Firlakuza [10]
3 years ago
5

Rewrite x^2 + 6x − 1 = 0 in the form (x + a)^2 = k, where a and k are constants. What is k?

Mathematics
1 answer:
Yuri [45]3 years ago
5 0

answer

10

step-by-step explanation

first find the (x+a)^2 part

using x^2 + 6x + c, we need to find the value c that completes the perfect square

to do this, divide 6 by two to find a in (x+a)^2

6/2 = 3 = a

c = a^2

c = 3^2 = 9

plug in values

x^2 + 6x + 9 = (x+3)^2

compare this to  x^2 + 6x − 1, and you can see there is a (9 - -1) = 10 difference, so subtract 10 from both sides

x^2 + 6x + 9 = (x+3)^2

x^2 + 6x + 9 - 10 = (x+3)^2 - 10

x^2 + 6x + - 1 = 0 = (x+3)^2 - 10

0 = (x+3)^2 - 10

(x+3)^2 = 10

k = 10

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Step-by-step explanation:

First we find the critical points:

x(x - 1)(x - 5) = 0

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Construct a Table of values:

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x                  <0        0          >0             <0           0

x - 1             <0       -1           >0              <0           0

x - 5            < 0       0          > 0             <0           0

x(x-1)(x-5)    < 0      0          >0              <0          0 

So the answers are x =< 0 or  1 =< x <= 5.

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The scenario above assumes she gets 50% off the sale price of $45, so saves $15+22.50 = $37.50 off the original price.

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