Solving $ax^2 + bx = c$
Learn how to solve Solving $ax^2 + bx = c$ with clear steps and practice problems for Grade 9 algebra. Build confidence solving equations and checking your solutions.
Key Concepts
Property When solving $ax^2 + bx = c$, you must first divide every term in the equation by the coefficient 'a'. This crucial first step ensures the $x^2$ coefficient is equal to 1, allowing you to proceed with completing the square as you normally would. Explanation Do not let a number in front of $x^2$ scare you. Your first mission is to eliminate it by dividing the whole equation by that number. Once the $x^2$ term is standing alone, you are back on familiar ground and can solve the problem. Examples $2x^2 + 8x = 10 \rightarrow x^2 + 4x = 5 \rightarrow (x+2)^2 = 5+4 \rightarrow (x+2)^2 = 9 \rightarrow x=1$ or $x= 5$. $3x^2 12x = 15 \rightarrow x^2 4x = 5 \rightarrow (x 2)^2 = 5+4 \rightarrow (x 2)^2 = 9 \rightarrow x=5$ or $x= 1$.
Common Questions
What is Solving $ax^2 + bx = c$ in Grade 9 math?
Solving $ax^2 + bx = c$ is a key algebra concept where students learn to apply mathematical rules and properties to solve problems. Understanding this topic builds skills needed for higher-level math.
How do you solve problems involving Solving $ax^2 + bx = c$?
Identify the given information, apply the relevant property or formula, simplify step by step, and check your answer. Practice with varied examples to build fluency.
Where is Solving $ax^2 + bx = c$ used in real life?
Solving $ax^2 + bx = c$ appears in fields like science, engineering, finance, and technology. Understanding this concept helps solve real-world problems that involve mathematical relationships.