Solution - Nonlinear equations
Other Ways to Solve:
Step by Step Solution
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
18*x^2+6-(4)=0
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((2•32x2) + 6) - 4 = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
18x2 + 2 = 2 • (9x2 + 1)
Polynomial Roots Calculator :
3.2 Find roots (zeroes) of : F(x) = 9x2 + 1
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 9 and the Trailing Constant is 1.
The factor(s) are:
of the Leading Coefficient : 1,3 ,9
of the Trailing Constant : 1
Let us test ....
| P | Q | P/Q | F(P/Q) | Divisor | |||||
|---|---|---|---|---|---|---|---|---|---|
| -1 | 1 | -1.00 | 10.00 | ||||||
| -1 | 3 | -0.33 | 2.00 | ||||||
| -1 | 9 | -0.11 | 1.11 | ||||||
| 1 | 1 | 1.00 | 10.00 | ||||||
| 1 | 3 | 0.33 | 2.00 | ||||||
| 1 | 9 | 0.11 | 1.11 |
Polynomial Roots Calculator found no rational roots
Equation at the end of step 3 :
2 • (9x2 + 1) = 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 : 9x2+1 = 0
Subtract 1 from both sides of the equation :
9x2 = -1
Divide both sides of the equation by 9:
x2 = -1/9 = -0.111
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ -1/9
In Math, i is called the imaginary unit. It satisfies i2 =-1. Both i and -i are the square roots of -1
Accordingly, √ -1/9 =
√ -1• 1/9 =
√ -1 •√ 1/9 =
i • √ 1/9
The equation has no real solutions. It has 2 imaginary, or complex solutions.
x= 0.0000 + 0.3333 i
x= 0.0000 - 0.3333 i
Two solutions were found :
- x= 0.0000 - 0.3333 i
- x= 0.0000 + 0.3333 i
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