### Rearrange:

Rearrange the equation by subtracting what is khổng lồ the right of the equal sign from both sides of the equation : x^3/2-(27)=0

## Step 1 :

x3 Simplify —— 2 Equation at the kết thúc of step 1 : x3 —— - 27 = 0 2

## Step 2 :

Rewriting the whole as an Equivalent Fraction :2.1Subtracting a whole from a fraction Rewrite the whole as a fraction using 2 as the denominator :

27 27 • 2 27 = —— = —————— 1 2 Equivalent fraction : The fraction thus generated looks different but has the same value as the whole Common denominator : The equivalent fraction & the other fraction involved in the calculation nội dung the same denominator

Adding fractions that have a common denominator :2.2 Adding up the two equivalent fractions showroom the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce to lớn lowest terms if possible:

x3 - (27 • 2) x3 - 54 ————————————— = ——————— 2 2 Trying to lớn factor as a Difference of Cubes:2.3 Factoring: x3 - 54 Theory : A difference of two perfect cubes, a3-b3 can be factored into(a-b)•(a2+ab+b2)Proof:(a-b)•(a2+ab+b2)=a3+a2b+ab2-ba2-b2a-b3 =a3+(a2b-ba2)+(ab2-b2a)-b3=a3+0+0-b3=a3-b3Check: 54 is not a cube !! Ruling:Binomial can not be factored as the difference of two perfect cubes

### Polynomial Roots Calculator :

2.4 Find roots (zeroes) of : F(x) = x3 - 54Polynomial Roots Calculator is a set of methods aimed at finding values ofxfor which F(x)=0 Rational Roots kiểm tra 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 integersThe Rational Root Theorem states that if a polynomial zeroes for a rational numberP/Q then p. Is a factor of the Trailing Constant and Q is a factor of the Leading CoefficientIn this case, the Leading Coefficient is 1 và the Trailing Constant is -54. The factor(s) are: of the Leading Coefficient : 1of the Trailing Constant : 1 ,2 ,3 ,6 ,9 ,18 ,27 ,54 Let us chạy thử ....

PQP/QF(P/Q)Divisor
-11 -1.00 -55.00
-21 -2.00 -62.00
-31 -3.00 -81.00
-61 -6.00 -270.00
-91 -9.00 -783.00
-181-18.00-5886.00
-271-27.00-19737.00
-541-54.00-157518.00
11 1.00 -53.00
21 2.00 -46.00
31 3.00 -27.00
61 6.00 162.00
91 9.00 675.00
181 18.00 5778.00
271 27.0019629.00
541 54.00157410.00

Polynomial Roots Calculator found no rational roots

Equation at the kết thúc of step 2 : x3 - 54 ——————— = 0 2

## Step 3 :

When a fraction equals zero :3.1 When a fraction equals zero ...Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.Here"s how:

x3-54 ————— • 2 = 0 • 2 2 Now, on the left hand side, the 2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.The equation now takes the shape:x3-54=0

Solving a Single Variable Equation:3.2Solve:x3-54 = 0Add 54 to both sides of the equation:x3 = 54 When two things are equal, their cube roots are equal.

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Taking the cube root of the two sides of the equation we get: x = ∛ 54 Can ∛ 54 be simplified ?Yes!The prime factorization of 54is2•3•3•3 khổng lồ be able to remove something from under the radical, there have khổng lồ be 3 instances of it (because we are taking a cube i.e. Cube root).∛ 54 =∛2•3•3•3 =3 •∛ 2 The equation has one real solutionThis solution is x = 3 • ∛2 = 3.7798