23.5 X square + 32.4 X + 425 is equals to zero by formula method
Answers
Step-by-step explanation:
Solving Quadratic Equations
Solving Quadratic Equations
Solving Quadratic Equations
A quadratic equation is an equation that could be written as
ax 2 + bx + c = 0
when a 0.
There are three basic methods for solving quadratic equations: factoring, using the quadratic formula, and completing the square.
Factoring
To solve a quadratic equation by factoring,
Put all terms on one side of the equal sign, leaving zero on the other side.
Factor.
Set each factor equal to zero.
Solve each of these equations.
Check by inserting your answer in the original equation.
Example 1
Solve x 2 – 6 x = 16.
Following the steps,
x 2 – 6 x = 16 becomes x 2 – 6 x – 16 = 0
Factor.
( x – 8)( x + 2) = 0
Setting each factor to zero, equation
Then to check, equation
Both values, 8 and –2, are solutions to the original equation.
Example 2
Solve y 2 = – 6 y – 5.
Setting all terms equal to zero,
y 2 + 6 y + 5 = 0
Factor.
( y + 5)( y + 1) = 0
Setting each factor to 0, equation
To check, y 2 = –6 y – 5
equation
A quadratic with a term missing is called an incomplete quadratic (as long as the ax 2 term isn't missing).
Example 3
Solve x 2 – 16 = 0.
Factor.
equation
To check, x 2 – 16 = 0
equation
Example 4
Solve x 2 + 6 x = 0.
Factor.
equation
To check, x 2 + 6 x = 0
equation
Example 5
Solve 2 x 2 + 2 x – 1 = x 2 + 6 x – 5.
First, simplify by putting all terms on one side and combining like terms.
equation
Now, factor.
equation
To check, 2 x 2 + 2 x – 1 = x 2 + 6 x – 5
equation
The quadratic formula
Many quadratic equations cannot be solved by factoring. This is generally true when the roots, or answers, are not rational numbers. A second method of solving quadratic equations involves the use of the following formula: equation
a, b, and c are taken from the quadratic equation written in its general form of
ax 2 + bx + c = 0
where a is the numeral that goes in front of x 2, b is the numeral that goes in front of x, and c is the numeral with no variable next to it (a.k.a., “the constant”).
When using the quadratic formula, you should be aware of three possibilities. These three possibilities are distinguished by a part of the formula called the discriminant. The discriminant is the value under the radical sign, b 2 – 4 ac. A quadratic equation with real numbers as coefficients can have the following: