Question

sq.3 solving quadratics using square roots
score: 12/25 answered: 13/25
question 17
solve $36(w-4)^2 - 18 = 7$.
give exact answers - no decimals. use a comma to separate your two answers.
$w = \square$
enter the solutions as reduced fractions or integers.
question help: video
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Explanation:

Step1: Isolate the squared term

Add 18 to both sides.
$$36(w-4)^2 = 7 + 18$$
$$36(w-4)^2 = 25$$

Step2: Solve for $(w-4)^2$

Divide both sides by 36.
$$(w-4)^2 = \frac{25}{36}$$

Step3: Take square roots of both sides

Recall square roots give two solutions.
$$w-4 = \pm\sqrt{\frac{25}{36}}$$
$$w-4 = \pm\frac{5}{6}$$

Step4: Solve for $w$

Add 4 to both sides, convert 4 to sixths.
$$w = 4 + \frac{5}{6},\ w = 4 - \frac{5}{6}$$
$$w = \frac{24}{6} + \frac{5}{6},\ w = \frac{24}{6} - \frac{5}{6}$$

Answer:

$\frac{29}{6}$, $\frac{19}{6}$