The values of x are x=6 and x=10.
Step-by-step explanation:
The given quadratic equation is [tex]4(x-8)^{2}-34= -18[/tex]
To solve the quadratic equation for the x values :
The right side of the equation must be zero. For this, add 18 on both sides of the equations.
⇒ [tex]4(x-8)^{2} -34+18 = -18+18[/tex]
⇒ [tex]4(x-8)^{2} - 16 = 0[/tex]
Now, divide the equation by 4 on both sides in order to further simplify the equation.
⇒ [tex](x-8)^{2} -4 = 0[/tex]
Expand the term [tex](x-8)^{2}[/tex] as the algebraic expression [tex](a-b)^{2} = a^{2} + b^{2} - 2ab[/tex]
⇒ [tex](x-8)^{2} = x^{2} + 8^{2} -16x[/tex]
⇒ [tex]x^{2} -16x + 64[/tex]
Replacing the term [tex](x-8)^{2}[/tex] as [tex]x^{2} -16x + 64[/tex]
⇒ [tex]x^{2} -16x + 64-4 = 0[/tex]
⇒ [tex]x^{2} -16x + 60 = 0[/tex]
Using the factorization method,
The roots of the above equation are -6,-10.
Therefore, the solution is (x-6)(x-10)= 0.
The values of x are x=6 and x=10.
