Example Card: Solving a Rearranged Quadratic Equation
Master Solving a Rearranged Quadratic Equation with step-by-step worked examples for Grade 9 math students. Practice identifying key patterns and apply techniques to solve problems accurately.
Key Concepts
Sometimes an equation needs a little tidying up before the quadratic formula can work its magic. This example will cover the key idea of rearranging equations.
Example Problem Use the quadratic formula to solve $x^2 11x = 24$ for $x$.
Step by Step 1. First, we must rearrange the equation into the standard form $ax^2 + bx + c = 0$. $$ x^2 11x + 24 = 0 $$ 2. Now we identify our coefficients: $a=1$, $b= 11$, and $c=24$. 3. Apply the quadratic formula. $$ x = \frac{ b \pm \sqrt{b^2 4ac}}{2a} $$ 4. Substitute the values for $a$, $b$, and $c$. $$ x = \frac{ ( 11) \pm \sqrt{( 11)^2 4(1)(24)}}{2(1)} $$ 5. Simplify the expression inside and outside the square root. $$ x = \frac{11 \pm \sqrt{121 96}}{2} $$ $$ x = \frac{11 \pm \sqrt{25}}{2} = \frac{11 \pm 5}{2} $$ 6. Find the two possible solutions for $x$. $$ x = \frac{11+5}{2} = \frac{16}{2} = 8 $$ $$ x = \frac{11 5}{2} = \frac{6}{2} = 3 $$ The solutions are $x = 8$ and $x = 3$.
Common Questions
What is Solving a Rearranged Quadratic Equation in Grade 9 math?
Solving a Rearranged Quadratic Equation 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 a Rearranged Quadratic Equation?
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 a Rearranged Quadratic Equation used in real life?
Solving a Rearranged Quadratic Equation appears in fields like science, engineering, finance, and technology. Understanding this concept helps solve real-world problems that involve mathematical relationships.