Find the solution to the following equation by transforming it into a perfect square trinomial. x2 – 12x = 64

1 answer:

8 0

$x^2-12x=64\\\\x^2-2\cdot6\cdot x=64\\\\(x^2-2\cdot6\cdot x+6^2)-6^2=64\\\\(x-6)^2-36=64\\\\(x-6)^2=64+36\\\\(x-6)^2=100\qquad|\sqrt{(\ldots)}\\\\\\x-6=-10\qquad\vee\qquad x-6=10\\\\x=-10+6\qquad\vee\qquad x=10+6\\\\\boxed{x=-4\qquad\vee\qquad x=16}$

Answer A)

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The series formed by using exponential property we get : $\frac{1}{2} , \frac{1}{4} , \frac{1}{8} ,\frac{1}{16} ,\frac{1}{32} ,\frac{1}{64} ,\frac{1}{128} ,\frac{1}{256} ,\frac{1}{512} ,\frac{1}{1024} .$

What is Exponential Property?

Properties of Exponents : It is also called power or degree.
It tells us how many times the base will be multiplied by itself.
The properties of exponents or laws of exponents are wont to solve problems involving exponents.
These properties also are considered as major exponents rules to be followed while solving exponents.

Using exponential property on given values we get,

$2^1=1/ 2\\2^2=1/4\\2^3=1/8\\2^4= 1/16\\2^5= 1/32\\2^6 = 1/64\\2^7 = 1/128\\2^8 = 1/256\\2^9 = 1/512\\2^10 = 1/1024\ ...$

Complete series using exponent property is: $\frac{1}{2} , \frac{1}{4} , \frac{1}{8} ,\frac{1}{16} ,\frac{1}{32} ,\frac{1}{64} ,\frac{1}{128} ,\frac{1}{256} ,\frac{1}{512} ,\frac{1}{1024} ,$