Question

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

x^2 - 5 = 4x

Answer 1

Answer:

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

Step-by-step 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.

Answer 2

Answer:

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

Step-by-step 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,

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

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

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

Substitute in (1) , we get,

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

$\Rightarrow x=\frac{-(-4)\pm\sqrt{(-4)^2-4\cdot 1 \cdot (-5)}}{2 \cdot 1}$

$\Rightarrow x=\frac{4\pm\sqrt{36}}{2}$

$\Rightarrow x=\frac{4\pm 6}{2}$

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

$\Rightarrow x_1=\frac{10}{2}$ and $\Rightarrow x_2=\frac{-2}{2}$

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

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