Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
The formula [tex]\( c = \left(\frac{b}{2}\right)^2 \)[/tex] is used to complete the square in algebra.
Here is a detailed, step-by-step explanation:
1. Understanding "Completing the Square":
"Completing the square" is a method used in algebra to transform a quadratic expression of the form [tex]\( ax^2 + bx + c \)[/tex] into a perfect square trinomial. A perfect square trinomial is an expression that can be written as the square of a binomial.
2. Form of the Quadratic Expression:
Consider the quadratic expression [tex]\( x^2 + bx \)[/tex]. To complete the square, we need to transform it into the form [tex]\( (x + d)^2 \)[/tex], where [tex]\( d \)[/tex] is some number related to [tex]\( b \)[/tex].
3. Isolate the Terms:
Start with the expression [tex]\( x^2 + bx \)[/tex].
4. Determine the Value to Complete the Square:
To find the appropriate number to add and subtract (i.e., the value of [tex]\( c \)[/tex]), we use the formula [tex]\( c = \left(\frac{b}{2}\right)^2 \)[/tex]. This value of [tex]\( c \)[/tex] is what makes the expression a perfect square trinomial.
5. Applying the Formula:
Using the value obtained from [tex]\( c = \left(\frac{b}{2}\right)^2 \)[/tex]:
[tex]\[ x^2 + bx + \left(\frac{b}{2}\right)^2 \][/tex]
This trinomial can now be written as a perfect square:
[tex]\[ \left(x + \frac{b}{2}\right)^2 \][/tex]
6. Example:
For instance, if [tex]\( b = 6 \)[/tex]:
[tex]\[ c = \left(\frac{6}{2}\right)^2 = 3^2 = 9 \][/tex]
The original expression [tex]\( x^2 + 6x \)[/tex] can be transformed into:
[tex]\[ x^2 + 6x + 9 \][/tex]
Which can be written as:
[tex]\[ (x + 3)^2 \][/tex]
Thus, the formula [tex]\( c = \left(\frac{b}{2}\right)^2 \)[/tex] is used to complete the square in algebra by transforming a quadratic expression into a perfect square trinomial.
Here is a detailed, step-by-step explanation:
1. Understanding "Completing the Square":
"Completing the square" is a method used in algebra to transform a quadratic expression of the form [tex]\( ax^2 + bx + c \)[/tex] into a perfect square trinomial. A perfect square trinomial is an expression that can be written as the square of a binomial.
2. Form of the Quadratic Expression:
Consider the quadratic expression [tex]\( x^2 + bx \)[/tex]. To complete the square, we need to transform it into the form [tex]\( (x + d)^2 \)[/tex], where [tex]\( d \)[/tex] is some number related to [tex]\( b \)[/tex].
3. Isolate the Terms:
Start with the expression [tex]\( x^2 + bx \)[/tex].
4. Determine the Value to Complete the Square:
To find the appropriate number to add and subtract (i.e., the value of [tex]\( c \)[/tex]), we use the formula [tex]\( c = \left(\frac{b}{2}\right)^2 \)[/tex]. This value of [tex]\( c \)[/tex] is what makes the expression a perfect square trinomial.
5. Applying the Formula:
Using the value obtained from [tex]\( c = \left(\frac{b}{2}\right)^2 \)[/tex]:
[tex]\[ x^2 + bx + \left(\frac{b}{2}\right)^2 \][/tex]
This trinomial can now be written as a perfect square:
[tex]\[ \left(x + \frac{b}{2}\right)^2 \][/tex]
6. Example:
For instance, if [tex]\( b = 6 \)[/tex]:
[tex]\[ c = \left(\frac{6}{2}\right)^2 = 3^2 = 9 \][/tex]
The original expression [tex]\( x^2 + 6x \)[/tex] can be transformed into:
[tex]\[ x^2 + 6x + 9 \][/tex]
Which can be written as:
[tex]\[ (x + 3)^2 \][/tex]
Thus, the formula [tex]\( c = \left(\frac{b}{2}\right)^2 \)[/tex] is used to complete the square in algebra by transforming a quadratic expression into a perfect square trinomial.
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.
