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Algebra 2

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Algebra 2

Lesson 5-5

Example 1 Equation with Rational Roots
Solve 2x2 – 36x + 162 = 32 by using the Square Root Property.

2x2 – 36x + 162 = 32 Original equation
2(x2 – 18x + 81) = 2(16) Factor out the GCF. x2 – 18x + 81 = 16 Divide each side by 2. (x – 9)2 = 16 Factor the perfect trinomial square. x – 9 = Square Root Property x – 9 = ±4 = 4 x = 9 ± 4 Add 9 to each side. x = 9 + 4 or x = 9 – 4 Write as two equations. x = 13 x = 5 Solve each equation.

The solution set is {5, 13}. You can check this result by using factoring to solve the original equation.

Example 2 Equation with Irrational Roots
Solve x2 + 10x + 25 = 108 by using the Square Root Property.

x2 + 10x + 25 = 108 Original equation (x + 5)2 = 108 Factor the perfect square trinomial. x + 5 = Square Root Property x = –5 ±6 Add –5 to each side; = 6 x = –5 + 6 or x = –5 – 6 Write as two equations. x ≈ 5.4 x ≈ –15.4 Use a calculator.

The exact solutions of this equation are –5 – 6 and –5 + 6. The approximate solutions are –15.4 and 5.4. Check these results by finding and graphing the related quadratic function.

x2 + 10x + 25 = 108 Original equation x2 + 10x – 83 = 0 Subtract 108 from each side. y = x2 + 10x – 83 Related quadratic function.

CHECK Use the ZERO function of a graphing calculator. The approximate zeros of the related function are –15.4 and 5.4.

Example 3 Complete the Square
Find the value of c that makes x2 –x + c a perfect square. Then write the trinomial as a perfect square.
Step 1|Find one half of.|• = |
|||
Step 2|Square the result of Step 1|= |
Step 3|Add the result of Step 2 to x2 –x|x2 –x + |
The trinomial x2 –x + can be written as.

Example 4 Solve an Equation by...

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