Solve for $$ x $$ using the square root property. $$ 4(p+6)^{2}-27=9 $$ $$ p= $$ Entry Tip: Do not use a decimal approximation for square roots. To enter a number like $$ 5 \sqrt{7} $$, type $$ 5^{*} $$ sqrt(7). Preview your answer before submitting! Furthere Tip: Write your answers as a list, with your answers separated by (a) comma(s). For example, if you get 4 and $$ -\frac{2}{3} $$ as your answers, then enter $$ 4,-2 / 3 $$ in the box.

Question

UpStudy AI · Accepted Answer

Solve the equation $$ 4(p+6)^{2}-27=9 $$.
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$4\left(p+6ight)^{2}-27=9$$
- step1: Expand the expression:
  $$4p^{2}+48p+117=9$$
- step2: Move the expression to the left side:
  $$4p^{2}+48p+108=0$$
- step3: Factor the expression:
  $$4\left(p+3ight)\left(p+9ight)=0$$
- step4: Divide the terms:
  $$\left(p+3ight)\left(p+9ight)=0$$
- step5: Separate into possible cases:
  $$\begin{align}&p+3=0\&p+9=0\end{align}$$
- step6: Solve the equation:
  $$\begin{align}&p=-3\&p=-9\end{align}$$
- step7: Rewrite:
  $$p_{1}=-9,p_{2}=-3$$
The solutions to the equation $$4(p+6)^{2}-27=9$$ using the square root property are $$p=-9$$ and $$p=-3$$.
$$ p = -9, -3 $$

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Algebra Questions