Subtract
6
6
from both sides of the equation.
x
2
−
7
x
=
−
6
x
2
-
7
x
=
-
6
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of
b
b
.
(
b
2
)
2
=
(
−
7
2
)
2
(
b
2
)
2
=
(
-
7
2
)
2
Add the term to each side of the equation.
x
2
−
7
x
+
(
−
7
2
)
2
=
−
6
+
(
−
7
2
)
2
x
2
-
7
x
+
(
-
7
2
)
2
=
-
6
+
(
-
7
2
)
2
Simplify the equation.
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x
2
−
7
x
+
49
4
=
25
4
x
2
-
7
x
+
49
4
=
25
4
Factor the perfect trinomial square into
(
x
−
7
2
)
2
(
x
-
7
2
)
2
.
(
x
−
7
2
)
2
=
25
4
(
x
-
7
2
)
2
=
25
4
Solve the equation for
x
x
.
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x
=
6
,
1
The formulas:
![\log_a (xy)=\log_a x + \log_a y \\ \log_a (\frac{x}{y})=\log_a x - \log_a y \\ \log_a (x^n)n \log_a x](https://tex.z-dn.net/?f=%5Clog_a%20%28xy%29%3D%5Clog_a%20x%20%2B%20%5Clog_a%20y%20%5C%5C%0A%5Clog_a%20%28%5Cfrac%7Bx%7D%7By%7D%29%3D%5Clog_a%20x%20-%20%5Clog_a%20y%20%5C%5C%0A%5Clog_a%20%28x%5En%29n%20%5Clog_a%20x)
Expand the expression:
![\log_b (\frac{m^2n}{p})=\log_b m^2 + \log_b n - \log_b p= 2 \log_b m+\log_b n - \log_b p](https://tex.z-dn.net/?f=%5Clog_b%20%28%5Cfrac%7Bm%5E2n%7D%7Bp%7D%29%3D%5Clog_b%20m%5E2%20%2B%20%5Clog_b%20n%20-%20%5Clog_b%20p%3D%202%20%5Clog_b%20m%2B%5Clog_b%20n%20-%20%5Clog_b%20p)
Plug the values into the expression:
SIMPLIFY:
−7p+7p^2+6(−3p^2+ −10)
DISTRIBUTE:
= -7p+-7p^2+(-6)(-3p^2)+(-6)(-10)
= -7p+ -7p^2+18p^2+60
COMBINE LIKE TERMS:
= -7p+ -7p^2+18p^2+60
= (-7p^2+ 18p^2)+(-7p)+(60)
ANSWER:
= 11p^2 - 7p + 60