Question

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.

x^2 - 6 = -x

Answer 1

The final answers are x = 2 OR x = -3.

Explanation:

Given the equation is x^2 -6 = -x

Rewriting it in quadratic form as:- x^2 +x -6 = 0.

a = 1, b = 1, c = -6.

Using Quadratic formula as follows:- x = ( -b ± √(b² -4ac) ) / (2a)

x = ( -1 ± √(1 -4*1*-6) ) / (2*1)

x = ( -1 ± √(1 +24) ) / (2)

x = ( -1 ± √(25) ) / (2)

x = ( -1 ± 5 ) / (2)

x = (-1+5) / (2) OR x = (-1-5) / (2)

x = 4/2 OR x = -6/2

x = 2 OR x = -3

Hence, final answers are x = 2 OR x = -3.

Answer 2

Thus, the two root of the given quadratic equation
`x^2-6=-x` is 2 and -3 .

Explanation:

Consider, the given Quadratic equation,
`x^2-6=-x`

This can be written as ,
`x^2+x-6=0`

We have to solve using quadratic formula,

For a given quadratic equation
`ax^2+bx+c=0` we can find roots using,

`x=(-b\pm√(b^2-4ac))/(2a)` ...........(1)

Where,
`√(b^2-4ac)` is the discriminant.

Here, a = 1 , b = 1 , c = -6

Substitute in (1) , we get,

`x=(-b\pm√(b^2-4ac))/(2a)`

`\Rightarrow x=(-(1)\pm√((1)^2-4\cdot 1 \cdot (-6)))/(2 \cdot 1)`

`\Rightarrow x=(-1\pm√(25))/(2)`

`\Rightarrow x=(-1\pm 5)/(2)`

`\Rightarrow x_1=(-1+5)/(2)` and
`\Rightarrow x_2=(-1-5)/(2)`

`\Rightarrow x_1=(4)/(2)` and
`\Rightarrow x_2=(-6)/(2)`

`\Rightarrow x_1=2` and
`\Rightarrow x_2=-3`

Thus, the two root of the given quadratic equation
`x^2-6=-x` is 2 and -3 .