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likoan [24]
2 years ago
5

Solve the following equation by factoring:9x^2-3x-2=0

Mathematics
1 answer:
olya-2409 [2.1K]2 years ago
7 0

Answer:

The two roots of the quadratic equation are

x_1= - \frac{1}{3} \text{ and } x_2= \frac{2}{3}

Step-by-step explanation:

Original quadratic equation is 9x^{2}-3x-2=0

Divide both sides by 9:

x^{2} - \frac{x}{3} - \frac{2}{9}=0

Add \frac{2}{9} to both sides to get rid of the constant on the LHS

x^{2} - \frac{x}{3} - \frac{2}{9}+\frac{2}{9}=\frac{2}{9}  ==> x^{2} - \frac{x}{3}=\frac{2}{9}

Add \frac{1}{36}  to both sides

x^{2} - \frac{x}{3}+\frac{1}{36}=\frac{2}{9} +\frac{1}{36}

This simplifies to

x^{2} - \frac{x}{3}+\frac{1}{36}=\frac{1}{4}

Noting that (a + b)² = a² + 2ab + b²

If we set a = x and b = \frac{1}{6}\right) we can see that

\left(x - \frac{1}{6}\right)^2 = x^2 - 2.x. (-\frac{1}{6}) + \frac{1}{36} = x^{2} - \frac{x}{3}+\frac{1}{36}

So

\left(x - \frac{1}{6}\right)^2=\frac{1}{4}

Taking square roots on both sides

\left(x - \frac{1}{6}\right)^2= \pm\frac{1}{4}

So the two roots or solutions of the equation are

x - \frac{1}{6}=-\sqrt{\frac{1}{4}}  and x - \frac{1}{6}=\sqrt{\frac{1}{4}}

\sqrt{\frac{1}{4}} = \frac{1}{2}

So the two roots are

x_1=\frac{1}{6} - \frac{1}{2} = -\frac{1}{3}

and

x_2=\frac{1}{6} + \frac{1}{2} = \frac{2}{3}

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X=y<br> x+2y =3<br> Solve using substitution
Zielflug [23.3K]

Answer:

Therefore the Final Solution is

x = 1 and y = 1

Step-by-step explanation:

Given:

x=y                ...............Equation ( 1 )

x+2y=3         ................Equation ( 2 )

To Find:

x = ?

y = ?

Solution:

Equating Equation  ( 1 ) in Equation ( 2 ) we get

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Now Substituting y = 1 in Equation ( 1 ) we get

x =1\\\\\therefore x=1

Therefore the Final Solution is

x = 1 and y = 1

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3 years ago
Morgan is reupholstering an old chair with two circular cushions. Each cushion has a circumference of 7. 85 feet. He will need t
kramer

The total fabric Morgan needs to cover the cushions will be 19.64 square feet.

It is given that each cushion has a circumference of 7.85 feet.

It is known that the circumference of a circle = 2πr, where 'r' is the radius of the circle.

2πr = 7.85

r = 1.25

<h3>What is an area of a circle?</h3>

area of a circle is πr².

now, we can calculate the area = π× 1.25² = 4.91 square feet

since each circular cushion has two circular faces so the total number of faces Morgan needs to cover will be 4.

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to get more about the area of a circle, refer to the link:

brainly.com/question/12069107

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