Given equation : [tex]5x^2−34x=−24[/tex]
Adding 24 on both sides, we get
[tex]5x^2-34x+24=-24+24[/tex]
[tex]5x^2-34x+24=0[/tex]
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.
[tex]\mathrm{Break\:the\:expression\:into\:groups}[/tex]
[tex]=\left(5x^2-4x\right)+\left(-30x+24\right)[/tex]
[tex]\mathrm{Factor\:out\:}x\mathrm{\:from\:}5x^2-4x\mathrm{:\quad }x\left(5x-4\right)[/tex]
[tex]\mathrm{Factor\:out\:}-6\mathrm{\:from\:}-30x+24\mathrm{:\quad }-6\left(5x-4\right)[/tex]
[tex]=x\left(5x-4\right)-6\left(5x-4\right)[/tex]
[tex]\left(x-6\right)\left(5x-4\right)=0[/tex]
Setting each factor equal to 0 and solve for x.
x-6 =0
x=6.
5x-4 =0.
5x = 4.
x=4/5.
