What is the solution of the equation sqrt 2x+13-5=x?

Mathematics

2 answers:

Tom [10]3 years ago

6 0

2x-x=-13+5
x=-8
I think so
Good luck

Shalnov [3]3 years ago

4 0

Answer: The solution is x = -2.

Step-by-step explanation: The given equation is as follows:

$\sqrt{2x+13}-5=x.$

We will be using the following algebraic identities:

$(i)~(a+b)^2=a^2+2ab+b^2,\\\\(ii)~(\sqrt{a+b})^2=a+b.$

The solution is as follows:

$\sqrt{2x+13}-5=x\\\\\Rightarrow \sqrt{2x+13}=x+5\\\\\Rightarrow (\sqrt{2x+13})^2=(x+5)^2\\\\\Rightarrow 2x+13=x^2+10x+25\\\\\Rightarrow x^2+8x+12=0\\\\\Rightarrow x^2+6x+2x+12=0\\\\\Rightarrow x(x+6)+2(x+6)=0\\\\\Rightarrow (x+2)(x+6)=0\\\\\Rightarrow x+2=0,~~~~~~x+6=0\\\\\Rightarrow x=-2,~-6.$

If we substitute x = -2, then

$L.H.S=\sqrt{2\times (-2)+13}-5=\sqrt9-5=3-5=-2=R.H.S.$

Ie we substitute x = -6, then

$L.H.S=\sqrt{2\times (-6)+13}-5=\sqrt1-5=1-5=-4\neq -6=x=R.H.S.$

Since x = -6 does not satisfy the given equation, so the solution is x = -2.

Thus, the solution is x = -2.

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