Rearrange this expression into quadratic form, ax^2 + bx + c = 0, and identify the values of a, b, and c. 0.20 = x^2 – 35x – 0.20 a = b =
The Correct Answer and Explanation is:
We are given the expression: 0.20=x2−35x−0.200.20 = x^2 – 35x – 0.200.20=x2−35x−0.20
Our goal is to rearrange it into the standard quadratic form, which is: ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0
Step 1: Move all terms to one side of the equation
First, subtract 0.20 from both sides to get all terms on the left side: 0.20−0.20=x2−35x−0.20−0.200.20 – 0.20 = x^2 – 35x – 0.20 – 0.200.20−0.20=x2−35x−0.20−0.20
This simplifies to: 0=x2−35x−0.400 = x^2 – 35x – 0.400=x2−35x−0.40
So, the equation becomes: x2−35x−0.40=0x^2 – 35x – 0.40 = 0x2−35x−0.40=0
Step 2: Identify the coefficients
Now that the equation is in the standard quadratic form ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0, we can easily identify the values of aaa, bbb, and ccc.
- The coefficient of x2x^2×2 is a=1a = 1a=1.
- The coefficient of xxx is b=−35b = -35b=−35.
- The constant term is c=−0.40c = -0.40c=−0.40.
Final Answer:
So, the quadratic equation is: x2−35x−0.40=0x^2 – 35x – 0.40 = 0x2−35x−0.40=0
And the values of the coefficients are:
- a=1a = 1a=1
- b=−35b = -35b=−35
- c=−0.40c = -0.40c=−0.40
Explanation
To solve a quadratic equation, we first need to rewrite it in the form ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0. This is necessary because many solution methods, like the quadratic formula, rely on identifying the coefficients aaa, bbb, and ccc. In this case, we simply moved all terms to one side of the equation, ensuring that the right-hand side equals zero. By doing this, we can immediately extract the values of aaa, bbb, and ccc, making it easy to apply other solution methods when needed.
