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# Intermediate Algebra

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H81

1. To complete the square on x in x2 + 6x, find one-half of , square it to get , and add to get ________________

2. Use factoring to solve the equation.
9y2 - 576 = 0
y = (smaller value)
y = (larger value)

3. Use factoring to solve the equation.
4t - 3 = t2
t = (smaller value)
t = (larger value)

4. Use the square root property to solve the following equation. (Enter solutions from smallest to largest.)

u =

u =

5. Use the square root property to solve the following equation. (Enter solutions from smallest to largest.)
(y - 1)2 = 16
y =
y =

6. Use the square root property to solve the following equation. (Enter solutions from smallest to largest.)

x =

x =

7. Use completing the square to solve the following equation. (Enter solutions from smallest to largest. If the solutions are complex, enter them from smallest to largest value of the imaginary part.)
x2 + 17x + 72 = 0
x =
x =

8. Use completing the square to solve the following equation. (Enter solutions from smallest to largest. If the solutions are complex, enter them from smallest to largest value of the imaginary part.)

p =

p =

H82

1. Use the quadratic formula to solve the following equation. (Enter solutions from smallest to largest. If the solutions are complex, enter them from smallest to largest value of the imaginary part.)

x =

x =

2. Use the quadratic formula to solve the equation.
x2 - 3x - 10 = 0
x = (smaller value)
x = (larger value)

3. Use the quadratic formula to solve the following equation. (Enter solutions from smallest to largest. If the solutions are complex, enter them from smallest to largest value of the imaginary part.)

w =

w =

4. Use the quadratic formula to solve the following equation. (Enter solutions from smallest to largest. If the solutions are complex, enter them from smallest to largest value of the imaginary part.)

x =

x =

5. Find a quadratic equation that has a solution set of {8, 6}. (Use the least possible coefficients.)
= 0

H83

1. Solve the following equation. (Enter solutions from smallest to largest. If a solution has a multiplicity of two, enter it in consecutive answer boxes.)

x =
x =
x =
x =

2. Solve the following equation. (Enter solutions from smallest to largest. If a solution has a multiplicity of two, enter it in consecutive answer boxes.)

x =
x =
x =
x =

https://brainmass.com/math/basic-algebra/intermediate-algebra-317544

#### Solution Preview

H81

1. To complete the square on x in x2 + 6x, find one-half of 6, square it to get 9, and add to both sides of the equation to get (x + 3)2 = 9

2. Use factoring to solve the equation.
Factor 9 ïƒ  9 (y2 - 64) = 0 ïƒ  divide both sides by 9 ïƒ  y2 - 64 = 0 ïƒ  Rearrange: y2 = 64 ïƒ  y is either 8 or - 8
9y2 - 576 = 0
y = -8 (smaller value)
y = 8 (larger value)

3. Use factoring to solve the equation.
Rearrange to get: t2 - 4t + 3 = 0, then factor for t and find two numbers that if you multiply them you get + 3 and if you add them you get -4 ïƒ  The numbers are -1 nd -3 ïƒ  (t - 1)(t - 3) = 0, therefore, t is either 1 or 3
4t - 3 = t2
t = 1 (smaller value)
t = 3 (larger value)

4. Use the square root property to solve the following equation. (Enter solutions from smallest to largest.)

u = + ïƒ–108 OR u = - ïƒ–108 ïƒ  ïƒ–108 can be written as 2ïƒ–27
u = - 2ïƒ–27

u = + 2 ïƒ–27

5. Use the square root property to solve the following equation. (Enter solutions from smallest to largest.)
Either y-1 = +4 ...

#### Solution Summary

Some example questions regarding solving second degree equations by factoring and completing the square.

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