Rearrange this expression into quadratic form, ax^2+bx+c = 0 0.20 = x^2/55 – x where a = 1, and identify the values of b and c. a = Number 1 b = Number 0.20 c = Number – 11
The Correct Answer and Explanation is :
We are given the equation:
[
0.20 = \frac{x^2}{55} – x
]
Step 1: Eliminate the fraction
To remove the fraction, multiply both sides of the equation by 55:
[
55 \times 0.20 = 55 \times \left( \frac{x^2}{55} – x \right)
]
This simplifies to:
[
11 = x^2 – 55x
]
Step 2: Rearrange into standard quadratic form
Now, move all terms to one side of the equation to put it into standard quadratic form, ( ax^2 + bx + c = 0 ). Subtract 11 from both sides:
[
x^2 – 55x – 11 = 0
]
Step 3: Identify the coefficients
Now, the equation is in the form ( ax^2 + bx + c = 0 ), where:
- ( a = 1 ) (the coefficient of ( x^2 )),
- ( b = -55 ) (the coefficient of ( x )),
- ( c = -11 ) (the constant term).
Step 4: Conclusion
The quadratic equation is ( x^2 – 55x – 11 = 0 ), where:
- ( a = 1 ),
- ( b = -55 ),
- ( c = -11 ).
To summarize:
- The quadratic form is ( x^2 – 55x – 11 = 0 ).
- The value of ( a ) is 1,
- The value of ( b ) is -55,
- The value of ( c ) is -11.
The explanation shows how we start by eliminating the fraction, then move the terms to one side of the equation to match the standard quadratic form. The key to identifying the coefficients is ensuring the equation is in the form ( ax^2 + bx + c = 0 ).