Using Substitution method ,
the solution of expression is either
x =( -5 +√21 )/2 or x = ( -5-√21 )/2.
Substitution method : In mathematics, the substitution method is generally used to solve a system of equations.
In this method, first solve the equation for one variable and substitute the value of the variable into the second equation.
Finally, solve the equation to find the value of the second variable.
We have given expression,
(x + 4)² – 3(x + 4) – 3 = 0
use substituion, a = (x+4)
then we get , a² - 3a - 3 = 0
the above equation is quadrtic equation.
we solve it by using the formula of finding roots of a quadratic equation.
formula for px² + qx + c = 0 quadratic equation is x =( -q +- √q²- 4qc )/2p
so, we have p= 1 , q = - 3 , c = -3
putting the values in above formula we get,
a ={ -(-3) +- √9 - 4×1(-3)}/2×1
=> a = { 3 +/- √21}/2
substitute, a= x+ 4 => x = a-4
=> x = (3 +- √21)/2 - 4 = 1/2 ( 3 +- √21 - 8)
=> x = 1/2( -5 +- √21)
either x = 1/2( -5+√21) or। x = 1/2(-5 -√21)
Hence, the solution for given equation are
x = (-5+√21)/2 or (-5-√21)/2
To learn more about Substitution , refer:
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