Question

I need help on those question please. Thank you. This is non-graded. :)

Answer 1

We have the next given equation:

`x^2+10x=3`

A) Use the method of completing the square and square roots:

First, equal the equation to zero:

`x^2+10x-3=0`

Now, take half of the x term and square it:

`(10\ast(1)/(2))^2=25`

Then add the result to both sides:

`x^2+10x-3+25=25`

Rewrite the perfect square on the left

`(x+5)^2=28`

Now, take the square root of both sides:

`√((x+5)^2)=\pm√(28)`

Simplify:

`\begin{gathered} x+5=\pm√(4\ast7) \\ x+5=\pm2√(7) \end{gathered}`

Finally, solve for x:

`x=-5\pm2√(7)`

B) Use the quadratic formula:

The quadratic formula is given by:

`x=(-b\pm√(b^2-4ac))/(2a)`

Use the form ax²+bx+c=0

Where

a=1

b=10

c=-3

Replacing:

`\begin{gathered} x=(-(10)\pm√(10^2-4(1)(-3)))/(2(1)) \\ x=(-10\pm√(100+12))/(2) \\ \end{gathered}`

Simplify the square root and then simplify the whole expression:

`\begin{gathered} x=(-10\pm√(16\ast7))/(2) \\ x=(-10\pm4√(7))/(2) \\ x=(2(-5\pm2√(7)))/(2) \\ x=-5\pm2√(7) \end{gathered}`