Answer: a≓6.969819675
Explanation: Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
a+3/a+7-2*a-4/a^2+3*a-28-(2-a/4-a)=0
Step by step solution :
STEP
1
:
a
Simplify —
4
Equation at the end of step
1
:
3 4 a
((((((a+—)+7)-2a)-————)+3a)-28)-((2-—)-a) = 0
a (a2) 4
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 4 as the denominator :
2 2 • 4
2 = — = —————
1 4
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2 • 4 - (a) 8 - a
——————————— = —————
4 4
Equation at the end of step
2
:
3 4 (8-a)
((((((a+—)+7)-2a)-————)+3a)-28)-(—————-a) = 0
a (a2) 4
STEP
3
:
Rewriting the whole as an Equivalent Fraction
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 4 as the denominator :
a a • 4
a = — = —————
1 4
Adding fractions that have a common denominator :
3.2 Adding up the two equivalent fractions
(8-a) - (a • 4) 8 - 5a
——————————————— = ——————
4 4
Equation at the end of step
3
:
3 4 (8-5a)
((((((a+—)+7)-2a)-————)+3a)-28)-—————— = 0
a (a2) 4
STEP
4
:
4
Simplify ——
a2
Equation at the end of step
4
:
3 4 (8-5a)
((((((a+—)+7)-2a)-——)+3a)-28)-—————— = 0
a a2 4
STEP
5
:
3
Simplify —
a
Equation at the end of step
5
:
3 4 (8-5a)
((((((a+—)+7)-2a)-——)+3a)-28)-—————— = 0
a a2 4
STEP
6
:
Rewriting the whole as an Equivalent Fraction
6.1 Adding a fraction to a whole
Rewrite the whole as a fraction using a as the denominator :
a a • a
a = — = —————
1 a
Adding fractions that have a common denominator :
6.2 Adding up the two equivalent fractions
a • a + 3 a2 + 3
————————— = ——————
a a
Equation at the end of step
6
:
(a2+3) 4 (8-5a)
(((((——————+7)-2a)-——)+3a)-28)-—————— = 0
a a2 4
STEP
7
:
Rewriting the whole as an Equivalent Fraction
7.1 Adding a whole to a fraction
Rewrite the whole as a fraction using a as the denominator :
7 7 • a
7 = — = —————
1 a
Polynomial Roots Calculator :
7.2 Find roots (zeroes) of : F(a) = a2 + 3
Polynomial Roots Calculator is a set of methods aimed at finding values of a for which F(a)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers a 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 3.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3