The solution of the given equation is w = 8.
What is the solution of the equation?
A solution to an equation is a number that can be plugged in for the variable to make a true number statement
What is the splitting middle term?
Splitting of the middle term is that we have to rewrite the middle term of the quadratic expression as the sum or difference of the two terms.
We have an equation
[tex]\sqrt{w^{2}+7w-39 } =\sqrt{10w+1}[/tex]
To find the solution of the above equation,
Square both the sides of the above equation and find the value of x by splitting the middle term.
[tex]\implies (\sqrt{w^{2} +7w-39} )^{2} =(\sqrt{10w+1} )^{2}[/tex]
[tex]\implies w^{2} + 7w - 39 = 10w + 1[/tex]
[tex]\implies w^{2} + 7w - 10w -39-1= 0[/tex]
[tex]\implies w^{2} -3w - 40 = 0[/tex]
[tex]\implies w^{2} -8w +5w - 40=0[/tex]
[tex]\implies w(w-8)+5(w-8)=0[/tex]
[tex]\implies (w+5)(w-8)=0[/tex]
[tex]\implies w = 8 \ or\ -5[/tex]
w = -5 is not possible because the root will give the imaginary values.
Hence, the value of w is 8.
Thus, option D is correct.
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