How To Solve Quadratic Equations

Quadratic Equations Definition
The quadratic equation is the equation whose rank is the highest of the variables is two.

Quadratic Equations General Forms

ax² + bx + c = 0

Information:
a ≠ 0 with a, b, c, ∈ rill number

Finding the solution of a quadratic equation means finding the value of x such that if the substituted value would satisfy that requirement. Solving the quadratic equation is also called the root of the quadratic equation.

How to Solve Quadratic Equations

Some ways that can be used to solve the quadratic equation include:

1. Factorization
2. Complete perfect squares
3. Quadratic formula

1. Solving Quadratic Equations by Factoring

Using the multiplication property of a rill number, that is, if two rill numbers are multiplied the result is zero. Thus, one of these numbers is zero or both equals zero.

if p x q = 0 then p = 0 or q = 0

Quadratic Equations Example

Look for the roots of x² + 2x - 8 = 0 !

Quadratic Equations Solution by Factoring

To solve the equation x² + 2x - 8 = 0, first find two numbers that meet the following conditions:
The multiplication result is equal to a x c
The sum result is equal to b

For example, two qualifying numbers are α and β, then:
αβ = ac
α + β  = b

Thus, the form factor is:
(ax + α)(ax + β) = 0

By dividing a on the left and right sides, it will get the original form.

From the equation x² + 2x - 8 = 0 is obtained:
a = 1
b = 2
c = -8

Find the two numbers that make the multiply result = 1 x (-8) = -8, and the sum result = 2. The eligible numbers are 4 and -2. So:

So the roots of x² + 2x - 8 = 0 are -4 and 2

2. Solving Quadratic Equations by Completing The Perfect Square

The quadratic equation ax² + bx + c = 0, is converted to equation in the following way:
Make sure the coefficient of x² is 1, if not divide by a number such that the coefficient becomes 1.
Add left and right sides with half coefficient of x then squared.
Make the left side into a quadratic form, while the right-hand side is manipulated, making it a simpler form.

Quadratic Equation Example

By completing the perfect squares find the roots of x² - 4x - 5 = 0!

Quadratic Equation Solution by Completing The Perfect Square

x² - 4x - 5 = 0
x² - 4x = 5
The coefficient of x² is 1

Add left and right sides with half coefficient of x then squared.

Make the left side into a quadratic form, while the right-hand side is manipulated, making it a simpler form.

So the roots of x² - 4x - 5 = 0 are 5 or -1

3. Solving Quadratic Equations Using Quadratic Formula

Here is the quadratic formula:

Quadratic Equation Example

Find the settlement of x² - 6x + 9 = 0 using the formula of squares!

Quadratic Equation Solution Using Quadratic Formula

From x² - 6x + 9 = 0 obtained:
a = 1
b = -6
c = 9

Then:

Then the roots of x² - 6x + 9 = 0 are 3.

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Referensi :

• To'Ali's book math group accounting and sales

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