Question

S1053323

h(x) = (x + 4)
Ivan needs to solve the following equation b(x) = 25
He writes
(x+4)² =25
x+4=5
x=1
This is not fully correct.
(c) Explain why.

Answer 1

`\textbf{$x$ can take two values $1$ or $-9$.}\\`

Explanation:

`\textup{Given, ${(x + 4)}^2 = 25$}\\\textup{If we take square root on both sides, then we would have:}\\$$ {(x+4)} = \pm √(25) = \pm 5 $$\\$ \implies x + 4 = 5 \hspace{15mm} $ or \hspace{15mm} $ x + 4 = -5 $\\$ \implies x = 1  \hspace{22mm} $  or \hspace{15mm} $x = -9 $ \\\textup{Verify your answer by expanding ${(x+4)}^2 = 25$}\\\textup{Solving this we get}\\$$ x^2 + 8x - 9 = 0 $$\\\textup{which again yields}\\$$ x = -9, 1 $$`