Question

What are the roots of the equation?

x2+24=14x

Enter your answers in the boxes.

x1=

x2=

Answer 1

To find the roots of the equation \( x^2 + 24 = 14x \), we first need to rearrange it into standard form:

\[
x^2 - 14x + 24 = 0
\]

Next, we can use the quadratic formula, which is given by:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

In our equation, the coefficients are:
- \( a = 1 \)
- \( b = -14 \)
- \( c = 24 \)

Now, we calculate the discriminant \( b^2 - 4ac \):

\[
b^2 - 4ac = (-14)^2 - 4(1)(24) = 196 - 96 = 100
\]

Now we plug this into the quadratic formula:

\[
x = \frac{-(-14) \pm \sqrt{100}}{2(1)} = \frac{14 \pm 10}{2}
\]

Calculating the two roots:

1. First root (\( x_1 \)):

\[
x_1 = \frac{14 + 10}{2} = \frac{24}{2} = 12
\]

2. Second root (\( x_2 \)):

\[
x_2 = \frac{14 - 10}{2} = \frac{4}{2} = 2
\]

Thus, the roots of the equation are:

\[
x_1 = 12, \quad x_2 = 2
\]

So the final answers are:

\[
x_1 = 12
\]
\[
x_2 = 2
\]