Question

Solve the equation algebraically
5rad(x+4) =absolute value (x-3)

Answer 1

\[5\sqrt{x+4}=\left| x-3 \right|\]

Answer 2

\(\large {
5\sqrt{x+4}=| x-3 |\\\quad\\ \implies
\begin{cases}
+(5\sqrt{x+4})=x-3\implies 5\sqrt{x+4}=x-3\\
5\sqrt{x+4}+3=x
\\\hline\\

-(5\sqrt{x+4})=x-3\implies -5\sqrt{x+4}=x-3\\
-5\sqrt{x+4}+3=x
\end{cases}
}\)


two cases, for an absolute value expression, thus two values for "x"
keep in mind you always have a + and - case with absolute value expressions

Answer 3

ok i got that but I still dont know how to solve this

Answer 4

ohh shoot... aehmm yeah... ok... we do have an "x" on the left side... I see

Answer 5

have you ... covered the factoring quadratics?

Answer 6

idk maybe

Answer 7

hmmm meaning, have you factored something like \(x^2+3x-4\) yet?

Answer 8

yeah

Answer 9

ok.. have you covered the quadratic formula yet?

Answer 10

yass

Answer 11

k

Answer 12

let us pick the 1st case, one sec

Answer 13

\(\bf 5\sqrt{x+4}=x-3\impliedby \textit{let us square both sides}
\\ \quad \\
(5\sqrt{x+4})^2=(x-3)^2\implies (5)^2(\sqrt{x+4})^2=x^2-6x+9
\\ \quad \\
25(x+4)=x^2-6x+9\implies 25x+100=x^2-6x+9
\\ \quad \\
0=x^2-31x-91\)

now, we end up with a quadratic equation

91 is a prime, pretty sure of that

so it won't factor nicely, so we could get the middle term of -6

so you'd need to use the quadratic formula for that

Answer 14

\(\bf 0=x^2-31x-91\qquad \qquad
\textit{quadratic formula}
\\ \quad \\

0={\color{blue}{ 1}}x^2{\color{red}{ -31}}x{\color{green}{ -91}}
\qquad \qquad
x= \cfrac{ - {\color{red}{ b}} \pm \sqrt { {\color{red}{ b}}^2 -4{\color{blue}{ a}}{\color{green}{ c}}}}{2{\color{blue}{ a}}}\)

Answer 15

now let use pick the 2nd case

\(\bf -5\sqrt{x+4}=x-3\impliedby \textit{let us square both sides}
\\ \quad \\
(-5\sqrt{x+4})^2=(x-3)^2\implies (-5)^2(\sqrt{x+4})^2=x^2-6x+9
\\ \quad \\
25(x+4)=x^2-6x+9\implies 25x+100=x^2-6x+9
\\ \quad \\
0=x^2-31x-91\)

notice, the -5, turns to a positive 25
and we end up with the same equation as the 1st case

so, using the quadratic formula for the 1st one, solves also the 2nd one

Answer 16

ok thank you sooooo much @jdoe0001

Answer 17

ywq

Answer 18

yw rather