Question

question 5 of 10, step 1 of 1 solve the following quadratic - like equation. ((x - 7)^2-14(x - 7)+48 = 0) answer how to enter your answer (opens in new window) or

Explanation:

Step1: Substitute $u = x-7$

Let $u = x-7$, then the equation becomes:
$u^2 - 14u + 48 = 0$

Step2: Factor the quadratic

Find two numbers that multiply to 48 and add to -14: -6 and -8.
$(u - 6)(u - 8) = 0$

Step3: Solve for $u$

Set each factor equal to 0:
$u - 6 = 0 \implies u = 6$
$u - 8 = 0 \implies u = 8$

Step4: Substitute back $u = x-7$

For $u=6$:
$x - 7 = 6 \implies x = 6 + 7 = 13$
For $u=8$:
$x - 7 = 8 \implies x = 8 + 7 = 15$

Answer:

$x=13$ or $x=15$