Question

7x2 + 2x-1=0 by completing square methods ​

Answer 1

Step-by-step explanation:

Hopefully it will be helpful

Answer 2

Answer:

Step-by-step explanation:

Given: 7x²+2x-1=0

To  find: Solution of equation using completing square method.

Solution:

Step 1:Take the constant to other side

7x²+2x=1

Step 2:Divide the equation by 7

$\frac{7x^{2}+2x }{7} =\frac{1}{7} \\ \\ x^{2} +\frac{2x}{7} =\frac{1}{7}$

Step 3: Manuplute the middle, so that both a and b can be identify from the identity (a+b)²=a²+2ab+b²

$(x)^{2} +2.x.\frac{1}{7}=\frac{1}{7}$

it is clear that a=x and b=1/7

Step 4: Add 1/49 both sides

$(x)^{2} +2.x.\frac{1}{7}+\frac{1}{49} =\frac{1}{7}+\frac{1}{49}$

or

$(x+\frac{1}{7} )^{2} =\frac{8}{49}$

or

$(x+\frac{1}{7} )^{2} =\left(\frac{2\sqrt{2} }{7}\right)^2$

Step 5: Taking square root both sides

$(x+\frac{1}{7} )=\pm\left(\frac{2\sqrt{2} }{7}\right)$

Step 6: Taking different sign find both values of x

$(x+\frac{1}{7} )=\left(\frac{2\sqrt{2} }{7}\right)\\\\x=\frac{2\sqrt{2}}{7}-\frac{1}{7}\\ \\ x=\frac{2\sqrt{2}-1 }{7}$

By the same way

$(x+\frac{1}{7} )=-\left(\frac{2\sqrt{2} }{7}\right)\\\\x=\frac{-2\sqrt{2}}{7}-\frac{1}{7}\\ \\ x=\frac{-2\sqrt{2}-1 }{7}$

Final Answer:

$\bold{x=\frac{2\sqrt{2}-1 }{7}}\\ \\ \bold{x=\frac{-2\sqrt{2}-1 }{7}}$

Hope it helps you.

To learn more on brainly:

1) Find the nature of the roots of the following quadratic equations. If real roots exist, find them:

(i) 2x² – 3x + 5 = 0 (ii) 3x² − 4√3x + 4 = 0 (iii) 2x² – 6x + 3 = 0

https://brainly.in/question/5484016

2) Solve the quadratic equation 3x2 + 7x + 1 = 0 by

the method of completing the square

https://brainly.in/question/11798176