Question

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

Answer 1

Answer:

Thus, the two root of the given quadratic equation $x^2+4=6x$ is 5.24 and 0.76 .

Step-by-step explanation:

Consider, the given Quadratic equation, $x^2+4=6x$

This can be written as ,  $x^2-6x+4=0$

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 = -6 , c = 4

Substitute in (1) , we get,

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

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

$\Rightarrow x=\frac{6\pm\sqrt{20}}{2}$

$\Rightarrow x=\frac{6\pm 2\sqrt{5}}{2}$

$\Rightarrow x={3\pm \sqrt{5}}$

$\Rightarrow x_1={3+\sqrt{5}}$ and $\Rightarrow x_2={3-\sqrt{5}}$

We know $\sqrt{5}=2.23607$(approx)

Substitute, we get,

$\Rightarrow x_1={3+2.23607}$(approx) and $\Rightarrow x_2={3-2.23607}$(approx)

$\Rightarrow x_1={5.23607}$(approx) and $\Rightarrow x_2=0.76393}$(approx)

Thus, the two root of the given quadratic equation $x^2+4=6x$ is 5.24 and 0.76 .

Answer 2

Answer:

The final answers are x = 5.24 OR x = 0.76

Step-by-step explanation:

Given the equation is x^2 +4 = 6x

Rewriting it in quadratic form as:- x^2 -6x 4 = 0.

a = 1, b = -6, c = 4.

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

x = ( 6 ± √(36 -4*1*4) ) / (2*1)

x = ( 6 ± √(36 -16) ) / (2)

x = ( 6 ± √(20) ) / (2)

x = ( 6 ± 4.47 ) / (2)

x = (6+4.47) / (2) OR x = (6-4.47) / (2)

x = 10.47/2 OR x = 1.53/2

x = 5.235 OR x = 0.765

Hence, final answers are x = 5.24 OR x = 0.76