Solving $x^2 + bx = c$
Solve incomplete quadratic equations by completing the square or factoring after rearranging to standard form. Master Grade 9 quadratic solving strategies.
Key Concepts
Property For an equation in the form $x^2+bx=c$, first complete the square by adding $(\frac{b}{2})^2$ to both sides. Then, factor the left side into a binomial square and solve by taking the square root of both sides. Explanation After you have completed the square, you get a simple $(x+k)^2=d$ format. Now you can free 'x' from its parentheses prison by taking the square root! Just do not forget the $\pm$ symbol, which gives you two possible answers. Examples $x^2 + 6x = 16 \rightarrow (x+3)^2 = 16+9 \rightarrow (x+3)^2 = 25 \rightarrow x+3=\pm5$, so $x=2$ or $x= 8$. $x^2 2x = 8 \rightarrow (x 1)^2 = 8+1 \rightarrow (x 1)^2 = 9 \rightarrow x 1=\pm3$, so $x=4$ or $x= 2$.
Common Questions
What are the key steps to solving $x^2 + bx = c$?
Identify the equation type, isolate the variable using inverse operations, and verify by substituting back into the original equation.
What common mistakes occur when solving $x^2 + bx = c$?
Applying operations to only one side, sign errors when moving terms, and not checking solutions in the original equation.
How is this skill applied in real problems?
These techniques model physical, financial, and geometric situations where unknown quantities must be found from given conditions.