Question

$\sqrt{2 } {x}^{2} + 7x + 5 \sqrt{2 } = 0$
to solve this quadratic equations by factorisation method
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Answer 1

$\huge \sf {\orange {\underline {\pink{\underline {A᭄ɴsᴡᴇʀ࿐ \ :- }}}}}$

A᭄ɴsᴡᴇʀ࿐ :−

$\sqrt{2 } {x}^{2} + 7x + 5 \sqrt{2 } = 0 \\ \sqrt{2 }{x}^{2} + 2x + 5x + 5 \sqrt{2} = 0 \\ \sqrt{2} \times x \times x + \sqrt{2} \times \sqrt{2} \times x + 5 \times x + 5 \times \sqrt{2} = 0 \\ \sqrt{2} x( x + \sqrt{2} ) + 5(x + \sqrt{2} ) = 0 \\ ( \sqrt{2} x + 5)(x + \sqrt{2} ) = 0$

hope it's helpful to you ☺️

Answer 2

Step-by-step explanation:

ANSWER:-

Given that:-

$\sqrt{2 } {x}^{2} + 7x + 5 \sqrt{2 } = 0$

We need to solve it by Factorisation method.

What we can do is apply middle term Factorisation.

Now, this question often scares us, the square roots especially right?

So, we can solve it simply if we observe that root 2 times root 2 equals 2.

So,

$\sf{ \sqrt{2} x^2 + 7x + 5 \sqrt{2}}$

$\sf{ \sqrt{2} x^2 + 5x + 2x + 5 \sqrt{2}}$

$\sf{ \sqrt{2}x (x + \sqrt{2}) + 5( x + \sqrt{2})}$

$\sf{ (x + \sqrt{2})(\sqrt{2}x + 5)}$

So,that's the required answer.

The only sole trick applied:-

7 was broken down into 5 and 2 and then added.