Non Linear Data

Non linear equation solver involves solving non linear equation with the help of formulas and it is mainly used to find the unknown variable value. The quadratic equation is one of the non linear equation in which it transforms the polynomial function into normal linear function. Non linear equation is also related with the families of vectors called vector spaces or non linear spaces. The following are the example problem deals with non linear equation solved with detailed solution.

Non linear equation solver example problems:

Example 1:

Solve the non linear quadratic equation.

√ (x ² – 11x+28) = 2

Solution:

Given function is

√ (x ² – 11x+28) = 2

Squaring on both sides, then the above equation becomes

[√ (x ² – 11x+28)] ² = (2) ²

And simplify.

x ² – 11x+28= 4

Make the above equation in factor form.

x ² – 11x + 24 =0

The above equation is in quadratic form with two solutions.

x = 3 and x = 8

Conclusion:

The given equation has two real values as solution x = 3 and x = 8.

Example 2:

Solve the non linear quadratic equation.

         y ² – 4y + 13 = 0
Solution:

Given equation is

y ² – 4y + 13 = 0

The discriminant is given as

D = b² - 4ac

= (-4)2 - 4(1)(13) = -36

Since the discriminant results negative, the square root of the discriminant value is a pure imaginary number.

√(D) = √(-36) = √(-1)√(36) = 6i

where i is the imaginary part defined as i = √(-1).

To find the solution we use b / 2a formula.

y₁ = (4 + 6i)) / (2*1) = 2 + 3i

y₂ = (4 - 6i) / (2*1) = 2 - 3i

Conclusion:

So the given equation has two imaginary solutions 2 + 3i and 2 – 3i.

Non linear equation solver practice problems:

1) Solve the non linear quadratic equation.
                      y ² + 9 = 0
Answer: (y – 3i) (y + 3i) is the solution.
2) Solve the non linear quadratic equation.
                         -y ² + 2y = -3
Answer: (y + 1) (y – 3) is the solution.