16.1 Solving Quadratics by square roots
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This document introduces the square root property and method for solving quadratic equations using square roots. It provides 3 steps: 1) isolate the term being squared, 2) take the square root of both sides, and 3) solve the remaining equation if needed. Examples are shown of solving equations of the form x^2=a, (x-b)^2=c, and (ax-b)^2=c by taking the square root and solving the resulting linear equations. It is noted that some quadratic equations using this method may have no real solutions.
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16.1 Solving Quadratics by square roots
- 1. Chapter 16.1 p. 563 Solving Quadratic Equations by the Square Root Property
- 2. Square Root Property We will be using factoring to solve quadratic equations in this chapter as well. This chapter will introduce additional methods for solving quadratic equations. Square Root Property If b is a real number and a2 = b, then ba ±=
- 3. STEPS TO SOLVE QUADRATICS WITH SQUARE ROOTS 1. Isolate what is being squared on one side of the equation EX: 2x2 + 2 = 4 -2 -2 2x2 = 2 ÷2 ÷2 x2 = 1 2. Take a square root of each side. √ x2 = √1 x = ± 1 3. Solve the remaining equation for x (if needed)
- 4. Solve x2 = 49 2±=x Solve (y – 3)2 = 4 Solve 2x2 = 4 x2 = 2 749 ±=±=x TWO OPTIONS: y – 3 = + 2 or y – 3 = - 2 y = 5 or y = 1 243 ±=±=−y Square Root Property Example
- 5. Solve x2 + 4 = 0 x2 = −4 There is no real solution because the square root of −4 is not a real number. Square Root Property Example
- 6. Solve (x + 2)2 = 25 x = −2 ± 5 x = −2 + 5 or x = −2 – 5 x = 3 or x = −7 5252 ±=±=+x Square Root Property Example
- 7. Solve (3x – 17)2 = 28 72173 ±=x 3 7217 ± =x 727428 ±=±=±3x – 17 = Square Root Property Example