Final answer:
The quadratic equation 5x²+18x-2=6 are x=2/5 and x=-4.
Step-by-step explanation:
To solve the quadratic equation 5x²+18x-2=6 by factoring, we can rearrange the equation to set it equal to zero:
5x²+18x-8=0
Next, we look for two numbers that multiply to give -40 (the product of the coefficients of x² and the constant term) and add up to 18 (the coefficient of x). In this case, the numbers are 20 and -2.
So we rewrite the middle term using these numbers:
5x²+20x-2x-8=0
Then, we factor by grouping:
(5x²+20x)+(-2x-8)=0
5x(x+4)-2(x+4)=0
(5x-2)(x+4)=0
Now, we set each factor equal to zero and solve for x:
5x-2=0 or x+4=0
5x=2 or x=-4
x=2/5 or x=-4
In summary, the quadratic equation 5x²+18x-2=6 can be solved by factoring. The solutions are x=2/5 and x=-4.