Question

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

x^2 - 6 = -x

Answer 1

Answer:

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

Step-by-step 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,

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$  ...........(1)

Where,  $\sqrt{b^2-4ac}$ is the discriminant.

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

Substitute in (1) , we get,

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$\Rightarrow x=\frac{-(1)\pm\sqrt{(1)^2-4\cdot 1 \cdot (-6)}}{2 \cdot 1}$

$\Rightarrow x=\frac{-1\pm\sqrt{25}}{2}$

$\Rightarrow x=\frac{-1\pm 5}{2}$

$\Rightarrow x_1=\frac{-1+5}{2}$ and $\Rightarrow x_2=\frac{-1-5}{2}$

$\Rightarrow x_1=\frac{4}{2}$ and $\Rightarrow x_2=\frac{-6}{2}$

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

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

Answer 2

Answer:

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

Step-by-step 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.