Question

question 6
for the following exercise, solve the quadratic equation by factoring.
$2x^2 + 2x - 24 = 0$
$x = $
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question 7
for the following exercise, solve the quadratic equation by using the quadratic formula.
$3x^2 + 8x - 16 = 0$
$x = $
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Explanation:

Question 6

Step1: Factor out common term

$2x^2 + 2x - 24 = 2(x^2 + x - 12) = 0$

Step2: Factor quadratic trinomial

$x^2 + x - 12 = (x+4)(x-3)$, so $2(x+4)(x-3)=0$

Step3: Solve for $x$

Set each factor to 0:
$x+4=0 \implies x=-4$
$x-3=0 \implies x=3$

Question 7

Step1: Identify quadratic coefficients

For $3x^2+8x-16=0$, $a=3$, $b=8$, $c=-16$

Step2: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:
$x=\frac{-8\pm\sqrt{8^2-4(3)(-16)}}{2(3)}$

Step3: Calculate discriminant

$\sqrt{64 + 192}=\sqrt{256}=16$

Step4: Solve for $x$

$x=\frac{-8+16}{6}=\frac{8}{6}=\frac{4}{3}$
$x=\frac{-8-16}{6}=\frac{-24}{6}=-4$

Answer:

Question 6: $x = -4, 3$
Question 7: $x = \frac{4}{3}, -4$