Honors Math 2 Solving Quadratic Equations – Extra Practice To solve a quadratic equation: -­‐ Set one side of the equation equal to 0 -­‐ Combine like terms, if necessary -­‐ Divide through by a common factor, if possible (only divide by constants, not variables) -­‐ Try to solve by factoring and ZPP -­‐ If not possible, use quadratic formula List of factoring techniques: -­‐ Greatest common factor -­‐ Difference of squares -­‐ Sum/product monic factoring -­‐ Completing the square -­‐ Scaling/z-­‐substitution -­‐ Splitting the middle term Practice Problems: Solve the following equations, if possible 1. 𝑥 ! − 7𝑥 = 18 2. 2𝑥 ! = 12𝑥 − 18 3. 3𝑦 ! + 7𝑦 + 4 = 0 4. 4𝑥 ! − 12𝑥 = 7 5. 𝑥 ! − 8𝑥 + 14 = 0 6. 10𝑥 − 4 = −𝑥 ! 7. (𝑥 + 1)! + 16 = 0 8. 4𝑥 ! − 25 = 0 9. 3𝑡 ! − 2 = −4𝑡 10. 𝑎! + 11𝑎 + 30 = 0 11. 9𝑥 ! + 18𝑥 − 16 = 0 12. 5𝑥 ! − 5 = 0 Answers (with suggested solving method) 1. 𝑥 = 9, −2 (sum/product) 2. 𝑥 = 3 (divide by 2, then sum/product) !
3. 𝑦 = −1, − ! (splitting middle term) !
!
4. 𝑥 = ! , − ! (z-­‐substitution) 5.
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𝑥 = 4 ± 2 (completing the square) 𝑥 = −5 ± 29 (completing the square) No solution (can’t factor sum of squares) !
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𝑥 = ! , − ! (difference of squares) !!± !"
9. 𝑡 = ! (quadratic formula) 10. 𝑎 = −6, −5 (sum/product) ! !
11. 𝑥 = − ! , ! (z-­‐substitution) 12. 𝑥 = 1, −1 (divide by 5 ,then difference of squares)