2^2x-5 = 128^x find x
Answers
Answer:
2*x^5-(128)=0
Step by step solution :
STEP
1
:
Equation at the end of step 1
2x5 - 128 = 0
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
2x5 - 128 = 2 • (x5 - 64)
Polynomial Roots Calculator :
3.2 Find roots (zeroes) of : F(x) = x5 - 64
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is -64.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4 ,8 ,16 ,32 ,64
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -65.00
-2 1 -2.00 -96.00
-4 1 -4.00 -1088.00
-8 1 -8.00 -32832.00
-16 1 -16.00 -1048640.00
-32 1 -32.00 -33554496.00
-64 1 -64.00 -1073741888.00
1 1 1.00 -63.00
2 1 2.00 -32.00
4 1 4.00 960.00
8 1 8.00 32704.00
16 1 16.00 1048512.00
32 1 32.00 33554368.00
64 1 64.00 1073741760.00
Polynomial Roots Calculator found no rational roots
Equation at the end of step
3
:
2 • (x5 - 64) = 0
STEP
4
:
Equations which are never true:
4.1 Solve : 2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
4.2 Solve : x5-64 = 0
Add 64 to both sides of the equation :
x5 = 64
x = 5th root of (64)
The equation has one real solution
This solution is x = 2 • 5th root of 2 = 2.2974
One solution was found :
x = 2 • 5th root of 2 = 2.2974
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