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!!! 13. $x^2 + 6x - 27 = 0$ 14. $x^2 - 10x + 21 = 0$ 15. $4x^2 - 81 = 0$ 16. $9x^2 - 49 = 0$ 17. $x^2 + 4x = 21$ 18. $x^2 - 10x + 49 = 4x + 1$

Explanation:

Step1: Rearrange to standard form

$x^2 + 4x - 21 = 0$

Step2: Factor the quadratic

$(x+7)(x-3)=0$

Step3: Solve for x

$x+7=0 \implies x=-7$
$x-3=0 \implies x=3$

Step1: Rearrange to standard form

$x^2 - 14x + 48 = 0$

Step2: Factor the quadratic

$(x-6)(x-8)=0$

Step3: Solve for x

$x-6=0 \implies x=6$
$x-8=0 \implies x=8$

Answer:

$\{-7, 3\}$

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