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Mastering Equation Solving: Factoring, Square Root Method, and Completing the Square

This comprehensive guide empowers students to solve equations with one variable using three key methods: factoring, the square root method, and completing the square (CTS). Students will engage with practical examples, including step-by-step solutions to quadratic equations. The section on the quadratic formula is included to ensure a deep understanding of its derivation and application. Dive in for a robust review filled with engaging problems that reinforce learning and build confidence in solving equations.

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Mastering Equation Solving: Factoring, Square Root Method, and Completing the Square

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  1. Are you Ready for More?! A.6: Solving Equations by: Factoring, Square Root Method and Completing the Square (CTS)!

  2. A.6: Solving Equations by: Factoring, Square Root Method and CTS! • The students (YOU!), will be able to: • Solve Equations in One Variable • Solve Eqns Using the Square Root Method • Solve Eqns by Completing the Square (CTS) • Obtain the Quadratic Formula

  3. A.6: Solving Equations by: Factoring, Square Root Method and CTS! • You are going to LOVE this! Who doesn’t like some good ‘ole review problems? • Ex1 Solve the following eqns by FACTORING: • a) 3x2 + 5x – 2 = 0 b) x3 + x2 – 20x = 0 • b) x3 = x2 d) x3- 2x2– 4x + 8 = 0

  4. A.6: Solving Equations by: Factoring, Square Root Method and CTS! • Ex2 Solve the following eqns by the SQUARE ROOT METHOD: • a) x2 – 5 = 0 b) (x + 2)2 = 1

  5. A.6: Solving Equations by: Factoring, Square Root Method and CTS! • Remember Completing the Square? If you start with x2 + mx, what do you add to both sides? • What, then, is your end result? • Do you remember how much fun this is?!

  6. A.6: Solving Equations by: Factoring, Square Root Method and CTS! • Ex3 Solve by Completing The Square: • a) x2 – 6x = 16 b) x2 + 3x = 0 c) 2x2 + 8x = 10

  7. A.6: Solving Equations by: Factoring, Square Root Method and CTS! • The Quadratic Formula: Consider the equation ax2 + bx + c = 0, • If b2 – 4ac < 0, then ___________________________________________________________________ • If b2 – 4ac 0, then __________________________________________________________________ • x = __________________________

  8. A.6: Solving Equations by: Factoring, Square Root Method and CTS! • Ex4 Solve by applying the Quadratic Formula: • a) 3x2 + 4 = -6x b) -2x2 + 7x = -9 HMWK #2

  9. A.6: Solving Equations by: Factoring, Square Root Method and CTS! • Did we hit the TARGET?: • Solve Equations in One Variable • Solve Eqns Using the Square Root Method • Solve Eqns by Completing the Square (CTS) • Obtain the Quadratic Formula

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