The squiring numbers and square root number has inverse relationship.The square root and the square cancel each other.The value of the variable x of the given quadratic equation is 12/5 or 2.4
The given equation in the problem is,
[tex]\sqrt{x^2+49} =x+5[/tex]
Square both side of the above equation,
[tex](\sqrt{x^2+49})^2 =(x+5)^2[/tex]
The squiring numbers and square root number has inverse relationship. The square root and the square cancel each other. Thus,
[tex]\begin{aligned}\\x^2+49 &=(x+5)^2\\x^2+49&=x^2+25+10x\\x^2-x^2+10x&=49-25\\10x&=24\\x&=\dfrac{24}{10} \\x&=\dfrac{12}{5} \\x&=2.4\end[/tex]
Hence the value of the variable x of the given quadratic equation is 12/5 or 2.4.
Learn more about the quadratic equation here;
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