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Square Root Property and Completing the Square: Solving Equations

Learn how to solve equations using the square root property and completing the square method. Understand when to complete the square to find the solutions.

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Square Root Property and Completing the Square: Solving Equations

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  1. Chapter 8 Section 1 The Square Root Property and Completing the Square

  2. Question • If x2 = 25, what is the x value? • How many solutions?

  3. Solve the equation

  4. Solve • (x – 1)2 = 5 • Note: If one can get the term squared, then taking the square root of both sides will . . .

  5. Completing the Square Completing the square will allow one to write a binomial squared, then the solution will come. To complete the square, observe x2 + 6x + 9 (x)2 (3)2 2(x)(3)

  6. Observe Complete the square: half 10 and square x2 – 10x Half 10 is 5 and square is 25 Thus, x2 – 10x + 25 Factor: (x – 5)2

  7. Determine the constant that should be added so that the binomial becomes a perfect square trinomial 4) 5) 6)

  8. Next • Once one complete the square, one can now solve the equation: x2 – 10x = 0 x2 – 10x + 25 = 25 (x – 5)2 = 25 x - 5 = x =10 or 0

  9. Solve the equation

  10. Summary • Use square root property to solve equations • Complete the square • Complete the square to solve equations.

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