Write in Standard Form 11x=3x^2-9
The question is asking you to rewrite the given equation in the standard form of a quadratic equation. The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants. You are required to manipulate the equation 11x = 3x^2 - 9 so that it has this form, by moving all terms to one side of the equation and arranging them in descending order according to the power of x.
$11 x = 3 x^{2} - 9$
Answer
Solution:
Step:1 Begin by transferring all terms to one side to set the equation to zero.
Step:1.1 Subtract $3x^2$ from each side to start moving terms.$11x - 3x^2 = -9$
Step:1.2 Then add $9$ to both sides to complete the transfer of terms.$11x - 3x^2 + 9 = 0$
Step:2 Ensure the polynomial is in standard form by ordering terms from highest to lowest degree and combining like terms if necessary.$ax^2 + bx + c = 0$
Step:3 Rearrange the terms so that the quadratic term is first, followed by the linear term and constant.$-3x^2 + 11x + 9 = 0$
Step:4
Knowledge Notes:
To solve the given problem, we need to understand the concept of standard form for a quadratic equation. The standard form of a quadratic equation is expressed as $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants, and $a \neq 0$. The process of writing an equation in standard form involves:
Ensuring that all terms are on one side of the equation and the other side is set to zero.
Arranging the terms in descending order of their degree, which means the highest power of $x$ comes first.
Simplifying the equation by combining like terms if necessary.
In the context of the given problem, we are asked to write the equation $11x = 3x^2 - 9$ in standard form. This involves moving all terms to one side and arranging them in descending order of the power of $x$. The process includes subtraction and addition to both sides of the equation to isolate the terms and set the equation to zero. Once the terms are arranged correctly, the equation will be in standard form.
