Question

x2+6x+7=0 completing square method

Answer 1

Hey friend!

Here is your answer:

To solve x² + 6x + 7 = 0 by completing square method

Information:

Steps : For ax² + bx + c = 0

• Step 1: Divide all terms by a .

• Step 2: Move the number term (c/a) to the right side of the equation.

• Step 3: Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation

Now,

$x^2 + 6x + 7 = 0$

$\implies x^{2} + 2 \ * \ 3x + 7 = 0$

$\implies x^{2} + 2 \ * \ 3 + 7 + 2 - 2 = 0$

$\implies x^{2} + 2 \ * \ 3 + 9 - 2 = 0$

$\implies (x + 3 )^{2} -2 = 0\\\\\implies (x + 3)^2 - (\sqrt{2})^2 = 0\\\\\implies (x + 3 - \sqrt{2})(x + 3 + \sqrt{2}) = 0\\\\\implies Either\ ( x + 3 - \sqrt{2} = 0 \ or \ (x + 3 + \sqrt{2}) = 0\\\\\implies Either\ x = \sqrt{2} - 3 \ or \ x = - 3 - \sqrt{2}$

Answer : x = √2 - 3, -3 - √2

I hope it helps you