Question

Solve the quadratic equation.
x^2–10=3x

Answer 1

To solve the quadratic equation \(x^2 - 10 = 3x\), we first rearrange it into the standard form \(ax^2 + bx + c = 0\).

1. Start with the original equation:
\[
x^2 - 10 = 3x
\]

2. Move all terms to one side of the equation:
\[
x^2 - 3x - 10 = 0
\]

Now we can apply the quadratic formula, which is given by:
\[
x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}
\]
where \(a = 1\), \(b = -3\), and \(c = -10\).

3. Calculate the discriminant (\(b^2 - 4ac\)):
\[
b^2 - 4ac = (-3)^2 - 4(1)(-10) = 9 + 40 = 49
\]

4. Now substitute values into the quadratic formula:
\[
x = \frac{{-(-3) \pm \sqrt{49}}}{2(1)} = \frac{{3 \pm 7}}{2}
\]

5. This gives us two solutions:
\[
x = \frac{{3 + 7}}{2} = \frac{10}{2} = 5
\]
\[
x = \frac{{3 - 7}}{2} = \frac{-4}{2} = -2
\]

Thus, the solutions to the quadratic equation are:
\[
x = 5 \quad \text{and} \quad x = -2
\]