Answer:
Explanation:
To solve the quadratic equation 5x^2 - 14x + 8 = 0 by factoring, we need to factorize the expression on the left side to find its roots.
1. Start by multiplying the coefficient of x^2 (5) with the constant term (8). In this case, 5 * 8 = 40.
2. We need to find two numbers whose product is 40 and whose sum is the coefficient of x (-14). After examining the factors of 40, we find that -10 and -4 meet these conditions, as -10 * -4 = 40 and -10 + (-4) = -14.
3. Rewrite the middle term (-14x) using these two numbers: -10x - 4x.
Now, we can rewrite the quadratic equation as follows:
5x^2 - 10x - 4x + 8 = 0
4. Group the terms and factor by grouping:
(5x^2 - 10x) + (-4x + 8) = 0
5x(x - 2) - 4(x - 2) = 0
(x - 2)(5x - 4) = 0
Now, we have factored the quadratic expression into two binomials: (x - 2) and (5x - 4).
5. Set each binomial equal to zero and solve for x:
x - 2 = 0 or 5x - 4 = 0
x = 2 or x = 4/5
Therefore, the solutions to the quadratic equation 5x^2 - 14x + 8 = 0 are x = 2 and x = 4/5.