Solve Nonlinearequations X^3+x^2=-9x-9 Tiger Algebra Solver

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : x^3+x^2-(-9*x-9)=0

Step by step solution :

Step 1 :

Checking for a perfect cube :

1.1 x3+x2+9x+9 is not a perfect cube

Trying to factor by pulling out :

1.2 Factoring: x3+x2+9x+9 Thoughtfully split the expression at hand into groups, each group having two terms :Group 1: x3+x2 Group 2: 9x+9 Pull out from each group separately :Group 1: (x+1) • (x2)Group 2: (x+1) • (9) -------------------Add up the two groups : (x+1) • (x2+9) Which is the desired factorization

Polynomial Roots Calculator :

1.3 Find roots (zeroes) of : F(x) = x2+9Polynomial 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 integersThe 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 CoefficientIn this case, the Leading Coefficient is 1 and the Trailing Constant is 9. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 ,3 ,9 Let us test ....

Polynomial Roots Calculator found no rational roots

Equation at the end of step 1 :

Step 2 :

Theory - Roots of a product :

2.1 A product of several terms equals zero.When a product of two or more terms equals zero, then at least one of the terms must be zero.We shall now solve each term = 0 separatelyIn other words, we are going to solve as many equations as there are terms in the productAny solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

2.2 Solve : x2+9 = 0Subtract 9 from both sides of the equation : x2 = -9 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get: x = ± √ -9 In Math, i is called the imaginary unit. It satisfies i2 =-1. Both i and -i are the square roots of -1 Accordingly, √ -9 = √ -1• 9 = √ -1 •√ 9 = i • √ 9 Can √ 9 be simplified ?Yes! The prime factorization of 9 is 3•3 To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).√ 9 = √ 3•3 = ± 3 • √ 1 = ± 3 The equation has no real solutions. It has 2 imaginary, or complex solutions. x= 0.0000 + 3.0000 i x= 0.0000 - 3.0000 i

Solving a Single Variable Equation :

2.3 Solve : x+1 = 0Subtract 1 from both sides of the equation : x = -1

Three solutions were found :

1. x = -1
2. x= 0.0000 - 3.0000 i
3. x= 0.0000 + 3.0000 i