Question

solve the following quadratic equations. remember to factor fully and show your solutions. each answer must be in set notation (i.e. use the fancy brackets). show your work!!!

1. ( x^2 + 10x + 25 = 0 )
2. ( x^2 - 8x + 16 = 0 )
3. ( x^2 + 4x + 3 = 0 )
4. ( x^2 + 11x + 24 = 0 )
5. ( x^2 + x - 2 = 0 )
6. ( x^2 - x - 20 = 0 )

Explanation:

Problem 7:

Step1: Factor perfect square trinomial

$x^2 + 10x + 25 = (x+5)^2 = 0$

Step2: Solve for x

$x+5=0 \implies x=-5$

Problem 8:

Step1: Factor perfect square trinomial

$x^2 - 8x + 16 = (x-4)^2 = 0$

Step2: Solve for x

$x-4=0 \implies x=4$

Problem 9:

Step1: Factor the quadratic trinomial

$x^2 + 4x + 3 = (x+1)(x+3) = 0$

Step2: Solve each factor

$x+1=0 \implies x=-1$; $x+3=0 \implies x=-3$

Problem 10:

Step1: Factor the quadratic trinomial

$x^2 + 11x + 24 = (x+3)(x+8) = 0$

Step2: Solve each factor

$x+3=0 \implies x=-3$; $x+8=0 \implies x=-8$

Problem 11:

Step1: Factor the quadratic trinomial

$x^2 + x - 2 = (x+2)(x-1) = 0$

Step2: Solve each factor

$x+2=0 \implies x=-2$; $x-1=0 \implies x=1$

Problem 12:

Step1: Factor the quadratic trinomial

$x^2 - x - 20 = (x-5)(x+4) = 0$

Step2: Solve each factor

$x-5=0 \implies x=5$; $x+4=0 \implies x=-4$

Answer:

1. $\{-5\}$
2. $\{4\}$
3. $\{-3, -1\}$
4. $\{-8, -3\}$
5. $\{-2, 1\}$
6. $\{-4, 5\}$