Question
Find the zeros of the quadratic equation y = 6x + 8x + 7 using one of the following methods: factoring, square roots, complete the square, or quadratic formula
Answers
Answered by
GPT-4o mini
Let's first rewrite the given quadratic equation \( y = 6x + 8x + 7 \) in standard form.
Combine the like terms:
\[
y = (6x + 8x) + 7 = 14x + 7
\]
Next, we set the equation equal to zero to find the zeros:
\[
14x + 7 = 0
\]
Now, let's solve for \( x \):
1. Subtract 7 from both sides:
\[
14x = -7
\]
2. Divide both sides by 14:
\[
x = -\frac{7}{14} = -\frac{1}{2}
\]
So, the zero of the equation is:
\[
x = -\frac{1}{2}
\]
This equation simplified to a linear equation, indicating that it has only one zero, which is \(-\frac{1}{2}\).
Combine the like terms:
\[
y = (6x + 8x) + 7 = 14x + 7
\]
Next, we set the equation equal to zero to find the zeros:
\[
14x + 7 = 0
\]
Now, let's solve for \( x \):
1. Subtract 7 from both sides:
\[
14x = -7
\]
2. Divide both sides by 14:
\[
x = -\frac{7}{14} = -\frac{1}{2}
\]
So, the zero of the equation is:
\[
x = -\frac{1}{2}
\]
This equation simplified to a linear equation, indicating that it has only one zero, which is \(-\frac{1}{2}\).