Find the value of y.

Solve the quadratic equation by completing the square.x ^ 2 + 16x + 59 = 0First, choose the appropriate form and fill in the bla

nikitadnepr [17]

Given:

There are given the quadratic equation:

$x^2+16x+59=0$

Explanation:

To find the value of x by using completing the square, first, we need to subtract 59 on both sides of the given equation:

So,

From the given equation:

$\begin{gathered} x^2+16x+59=0 \\ x^2+16x+59-59=0-59 \\ x^2+16x=-59 \end{gathered}$

Now,

Take half of the x term and square it:

So,

From the x term,

$\lbrack16\cdot\frac{1}{2}\rbrack^2=64$

Then,

Add 64 on both sides of the above equation.

So,

$\begin{gathered} x^2+16x=-59 \\ x^2+16x+64=-59+64 \\ x^2+16x+64=5 \\ (x+8)^2=5 \end{gathered}$

Hence, an option first is correct:

$(x+8)^2=5$

Now,

From the above square:

$\begin{gathered} (x+8)^2=5 \\ x+8=\pm\sqrt[]{5} \end{gathered}$

Then,

Subtract 8 from both sides of the equation;;

So,

$\begin{gathered} x+8=\pm\sqrt[]{5} \\ x+8-8=\pm\sqrt[]{5}-8 \\ x=\pm\sqrt[]{5}-8 \\ x=\sqrt[]{5}-8,\pm\sqrt[]{5}-8 \\ x=-5.7639,-10.236067 \end{gathered}$

Final answer:

Hence, the value of x is shown below:

$x=(-5.76,-10.24)$

4 0

1 year ago

How do you factor 2x^2-9x-5?

maks197457 [2]

Hello from MrBillDoesMath!

Answer: (2x + 1) (x-5)

Discussion:

To factor the polynomial let's find its roots using the quadratic formula:

x = ( -b -+\- sqrt ( b^2 - 4ac)) / 2a which in our case is:

x = ( - (-9) +\- sqrt ( (-9^2 - 4*2*(-5)) ) /(2*2)

x = ( 9 +\- sqrt (81 + 40))/4 =>

x = ( 9 +\- sqrt(121)) / 4 =>

x = ( 9 +\- 11) /4 as sqrt (121) =11

Finally then,

x = ( 9 - 11) /4 = -2/4 = -1/2 and

x = (9 + 11)/4 = 20/4 = 5

So the polynomial factors as follows:

( 2x - (-1) ) ( x - 5) or

(2x + 1) (x-5)

Thank you,

MrB

7 0

3 years ago

Please help! Picture Down Below!

guajiro [1.7K]

Angle 4 = Angle 5 = 42⁰( alternate interrior angle)

Hope it helps u

5 0

3 years ago

Simplify this question

Lera25 [3.4K]

Answer:

decimal form: 1.88982236505

Hope This Helps! Have A Nice Day!!

4 0

4 years ago

Landen spent LL hours at the beach last weekend. Matéo spent 15\%15% fewer hours at the beach than Landen did. Which of the foll

ivanzaharov [21]

Answer: 0.85 L or $\frac{85L}{100}$ or $\frac{17L}{20}$

Step-by-step explanation:

Since, According to the question,

Landen spent time at the beach last weekend = L hours

And, Matéo spent 15% fewer hours at the beach than Landen did.

Therefore, Number of hours spent by Matéo = (Time spent by Landen last week - 15 % of the Time spent by Landen last week ) hours

= 85% of the Time spent by Landen last week

= $\frac{85\times L}{100}$

= $\frac{85L}{100}$ Hours

= $\frac{17L}{20}$ Hours

= 0.85 L Hours

8 0

4 years ago

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