Question

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

x^2 - 5 = 4x

Answer 1

Thus, the two root of the given quadratic equation
`x^2-5=4x` is 5 and -1 .

Explanation:

Consider, the given Quadratic equation,
`x^2-5=4x`

This can be written as ,
`x^2-4x-5=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 = -4 , c = -5

Substitute in (1) , we get,

`x=(-b\pm√(b^2-4ac))/(2a)`

`\Rightarrow x=(-(-4)\pm√((-4)^2-4\cdot 1 \cdot (-5)))/(2 \cdot 1)`

`\Rightarrow x=(4\pm√(36))/(2)`

`\Rightarrow x=(4\pm 6)/(2)`

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

`\Rightarrow x_1=(10)/(2)` and
`\Rightarrow x_2=(-2)/(2)`

`\Rightarrow x_1=5` and
`\Rightarrow x_2=-1`

Thus, the two root of the given quadratic equation
`x^2-5=4x` is 5 and -1 .

Answer 2

The final answers are x = 5 OR x = -1.

Explanation:

Given the equation is x^2 -5 = 4x

Rewriting it in quadratic form as:- x^2 -4x -5 = 0.

a = 1, b = -4, c = -5.

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

x = ( 4 ± √(16 -4*1*-5) ) / (2*1)

x = ( 4 ± √(16 +20) ) / (2)

x = ( 4 ± √(36) ) / (2)

x = ( 4 ± 6 ) / (2)

x = (4+6) / (2) OR x = (4-6) / (2)

x = 10/2 OR x = -2/2

x = 5 OR x = -1

Hence, final answers are x = 5 OR x = -1.