Question

100 POINTS I WILL MARK BRAINLIST

Answer 1

Answer:

$x=-4\pm2\sqrt{6}$

Step-by-step explanation:

Completing the square for quadratic in the form  $ax^2+bx+c=0$

Given equation:

$3x^2+24x-24=0$

Factor out 3:

$\implies 3(x^2+8x-8)=0$

Divide both sides by 3:

$\implies x^2+8x-8=0$

Add 8 to both sides:

$\implies x^2+8x=8$

$\textsf{Add }\: \left(\dfrac{b}{2}\right)^2\: \textsf{ to both sides}:$

$\implies x^2+8x+\left(\dfrac{8}{2}\right)^2=8+\left(\dfrac{8}{2}\right)^2$

$\implies x^2+8x+16=8+16$

$\implies x^2+8x+16=24$

Factor the left side:

$\implies (x+4)^2=24$

Square root both sides:

$\implies x+4=\pm2\sqrt{6}$

Subtract 4 from both sides:

$\implies x=-4\pm2\sqrt{6}$

Answer 2

Answer:

$\boxed{\sf x = -4 \pm 2\sqrt{6} }$

Explanation:

3x² + 24x - 24 = 0

factor the coefficient

3(x² + 8x) -24 = 0

Halve the second term and square it

3(x + 4)² -24 -3(4)² = 0

simplify the answer

3(x + 4)² -72 = 0

add 72 on both sides

3(x + 4)² = 72

divide both sides by 3

(x + 4)² = 24

square root both sides

x + 4 = ±√24

subtract both sides by 4

x = -4 ± 2√6