(7x - 5) (x + 3) solve value of X

Answer 1

To solve for the value of x, we need to expand the given expression:

(7x - 5)(x + 3)

Using the distributive property, we multiply each term in the first parentheses by each term in the second parentheses:

7x * x = 7x^2
7x * 3 = 21x
-5 * x = -5x
-5 * 3 = -15

Combining like terms, we obtain:

7x^2 + 21x - 5x - 15

Simplifying further:

7x^2 + 16x - 15

Now that we have a quadratic expression, we need to set it equal to zero in order to solve for x:

7x^2 + 16x - 15 = 0

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac))/(2a)

In our case, a = 7, b = 16, and c = -15:

x = (-16 ± √(16^2 - 4(7)(-15)))/(2(7))

Simplifying inside the square root:

x = (-16 ± √(256 + 420))/14

x = (-16 ± √676)/14

Taking the square root:

x = (-16 ± 26)/14

Now, we have two possible solutions for x:

x₁ = (-16 + 26)/14 = 10/14 = 5/7

x₂ = (-16 - 26)/14 = -42/14 = -3

Therefore, the values of x that solve the given expression are 5/7 and -3.