3 (9.) Express $$ -x^{2}+4 x+1 $$ in the form $$ -(x-p)^{2}+q $$. $$ \begin{array}{l} =-(x-p)^{2}+q \ =-\left[(x-2)^{2}-2^{2}-4 x-1\right] \ =-\left[(x-2)^{2}-5\right. \ =-(x-2)^{2}+5 \end{array} $$ Name 1 Answer $$ \qquad $$ [2] 0) Hence solve the equation $$ -x^{2}+4 x+1=0 $$, giving your answers correct to two decimal places.

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UpStudy AI · Accepted Answer

To solve the equation $$ -x^{2} + 4x + 1 = 0 $$ by expressing it in the form $$ -(x - p)^{2} + q $$, you've correctly completed the square and obtained:

$$
-(x - 2)^{2} + 5 = 0
$$

Now, solve for $$ x $$:

$$
-(x - 2)^{2} + 5 = 0 \
(x - 2)^{2} = 5 \
x - 2 = \pm \sqrt{5} \
x = 2 \pm \sqrt{5}
$$

Calculating the decimal values:

$$
\sqrt{5} \approx 2.23607
$$

So the solutions are:

$$
x = 2 + 2.23607 \approx 4.24 \
x = 2 - 2.23607 \approx -0.24
$$

**Answer:**

The solutions are $$ x = 4.24 $$ and $$ x = -0.24 $$.
The solutions are $$ x = 4.24 $$ and $$ x = -0.24 $$.

3 (9.) Express in the form .

Name
1
Answer
[2]
0) Hence solve the equation , giving your answers correct to two decimal places.

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3 (9.) Express in the form . Name 1 Answer [2] 0) Hence solve the equation , giving your answers correct to two decimal places.