Answer:
x = ± ∜175 = ± 3.6371
Explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x^4-(175)=0
Step by step solution :
STEP
1
:
Trying to factor as a Difference of Squares:
1.1 Factoring: x4-175
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 175 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Polynomial Roots Calculator :
1.2 Find roots (zeroes) of : F(x) = x4-175
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 -175.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,5 ,7 ,25 ,35 ,175
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -174.00
-5 1 -5.00 450.00
-7 1 -7.00 2226.00
-25 1 -25.00 390450.00
-35 1 -35.00 1500450.00
-175 1 -175.00 937890450.00
1 1 1.00 -174.00
5 1 5.00 450.00
7 1 7.00 2226.00
25 1 25.00 390450.00
35 1 35.00 1500450.00
175 1 175.00 937890450.00
Polynomial Roots Calculator found no rational roots
Equation at the end of step
1
:
x4 - 175 = 0
STEP
2
:
Solving a Single Variable Equation:
2.1 Solve : x4-175 = 0
Add 175 to both sides of the equation :
x4 = 175
x = ∜ 175
The equation has two real solutions
These solutions are x = ± ∜175 = ± 3.6371
Two solutions were found :
x = ± ∜175 = ± 3.6371