Question

given the equation x²-8x-30=3, solve the equation by completing the square. be sure to put the correct + or - sign in front of your answer. x²-8x ___= 33 ___(____)²=____so, x-4=___ and x-4=___x=___ and x=___

Answer 1

In the first part, they added 30 on both sides of the equation. Now, to complete the square we have to find a number that will make a perfect square.

We have 8x in the second term. 8 is 2*4, so if we add 16 on both sides of the equation we'll have a perfect square on the left:

- For the first two blanks:

x² - 8x + 16 = 33 + 16

-The next step is:

( x - 4 )² = 49

To solve this we have to take square root:

`\begin{gathered} x-4=\pm\sqrt[]{49} \\ x-4=\pm7 \end{gathered}`

- So, x - 4 = 7 and x- 4 = -7

Finally, we have to add 4 on both expressions to find the value of x:

`\begin{gathered} x=7+4=11 \\ x=-7+4=-3 \end{gathered}`

- x = 11 and x = -3