Question

Solve the equation by using the Square Root Property. 16x2 + 16x + 4 = 81

Answer 1

Answer:

$x = \dfrac{7}{4}, x = \dfrac{-11}{4}$              

Step-by-step explanation:

We are given the following equation in the question:

$16x^2 + 16x + 4 = 81$

We have to find the solution of the equation using square root property.

We can solve the equation as:

$16x^2 + 16x + 4 = 81\\(4x)^2 + 2(4x)(2) + (2)^2 = 81\\\text{Identity: }(a+b)^2 = a^2 + b^2 + 2ab\\\Rightarrow (4x+2)^2 = 81\\ \Rightarrow (4x+2) = \sqrt{81}\\ \Rightarrow (4x+2) = \pm 9\\ \Rightarrow (4x+2) = 9, (4x+2) = -9\\\Rightarrow 4x = 7, 4x = -11\\\Rightarrow x = \dfrac{7}{4}, x = \dfrac{-11}{4}$

is the required solution of the equation.