Question

solve the following equation using tables.
$5x^2 - 18x = -13$

$x = \square$
(use a comma to separate answers as needed.)

Explanation:

Step1: Rearrange to standard quadratic form

$5x^2 - 18x + 13 = 0$

Step2: Factor the quadratic expression

$(5x - 13)(x - 1) = 0$

Step3: Solve for x (zero product rule)

Set each factor equal to 0:
$5x - 13 = 0 \implies x = \frac{13}{5}$
$x - 1 = 0 \implies x = 1$
(To verify with tables, we can test values around these roots:
For $x=1$: $5(1)^2 -18(1) = 5-18=-13$, which matches the right-hand side.
For $x=\frac{13}{5}=2.6$: $5(2.6)^2 -18(2.6)=5(6.76)-46.8=33.8-46.8=-13$, which also matches.)

Answer:

$1, \frac{13}{5}$