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Ainat [17]
2 years ago
9

100 POINTS I WILL MARK BRAINLIST

Mathematics
2 answers:
AlladinOne [14]2 years ago
6 0

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}

salantis [7]2 years ago
5 0

Answer:

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

Explanation:

3x² + 24x - 24 = 0

<u>factor the coefficient</u>

3(x² + 8x) -24 = 0

<u>Halve the second term and square it</u>

3(x + 4)² -24 -3(4)² = 0

<u>simplify the answer</u>

3(x + 4)² -72 = 0

<u>add 72 on both sides</u>

3(x + 4)² = 72

<u>divide both sides by 3</u>

(x + 4)² = 24

<u>square root both sides</u>

x + 4 = ±√24

<u>subtract both sides by 4</u>

x = -4 ± 2√6

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