Question

SOLVE THIS PLZ 5x2−34x=−24

Answer 1

Given equation :
`5x^2−34x=−24`

Adding 24 on both sides, we get

`5x^2-34x+24=-24+24`

`5x^2-34x+24=0`

Let us factor this.

5*24 = 120.

b=-34.

So, we need to find the factors of 120 that add upto -34.

-30 and -4 are the factors add upto -34 and product 120.

`\mathrm{Break\:the\:expression\:into\:groups}`

`=\left(5x^2-4x\right)+\left(-30x+24\right)`

`\mathrm{Factor\:out\:}x\mathrm{\:from\:}5x^2-4x\mathrm{:\quad }x\left(5x-4\right)`

`\mathrm{Factor\:out\:}-6\mathrm{\:from\:}-30x+24\mathrm{:\quad }-6\left(5x-4\right)`

`=x\left(5x-4\right)-6\left(5x-4\right)`

`\left(x-6\right)\left(5x-4\right)=0`

Setting each factor equal to 0 and solve for x.

x-6 =0

x=6.

5x-4 =0.

5x = 4.

x=4/5.

Therefore, final answer is x=6, 4/5.