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Bot GPT 3.5 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.