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Question

# Solve the equation.$( a - 5 ) ^ { 2 } - 4 ( a - 5 ) - 21 = 0$

Solution

Verified
Step 1
1 of 4

The given equation is quadratic in $a-5$.

Let $t$ be the expression in the brackets to make the equation quadratic in $t$:

$t=a-5$

Make the substitution:

$t^2-4t-21=0$

The substituted equation has the form:

$xt^2+yt+z=0$

where:

$x=1 \qquad y=-4 \qquad z=-21$

The standard notation for $x$, $y$, and $z$ are $a$, $b$, and $c$, but $a$ is a variable in this task so we cannot use this notation to avoid confusion.

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