Question

Solve the equations for all values of x by completing the square x^2+62=-16x

Answer 1

`x = √(2) - 8\\x = -√(2) - 8`

Explanation:

To complete the square, we first have to get our equation into
`ax^2 + bx = c` form.

First we add 16x to both sides:

`x^2 + 16x + 62 = 0`

And now we subtract 62 from both sides.

`x^2 + 16x = -62`

We now have to add
`((b)/(2))^2` to both sides of the equation. b is 16, so this value becomes
`(16/2)^2 = 8^2 = 64`.

`x^2 + 16x + 64 = -62+64`

We can now write the left side of the equation as a perfect square. We know that x+8 will be the solution because
`8\cdot8=64` and
`8+8=16`.

`(x+8)^2 = -62 + 64`

We can now take the square root of both sides.

`x+8 = √(-62+64)\\\\ x+8 = \pm √(2)`

We can now isolate x on one side by subtracting 8 from both sides.

`x = \pm√(2) - 8`

So our solutions are

`x = √(2) - 8\\x = -√(2) - 8`

Hope this helped!