The expression provided is \( 5x^2 + x - 18 \). This is a quadratic expression in standard form: \( ax^2 + bx + c \), where \( a = 5 \), \( b = 1 \), and \( c = -18 \).

If you'd like to solve the equation \( 5x^2 + x - 18 = 0 \), we can use the quadratic formula:

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

Substituting the values \( a = 5 \), \( b = 1 \), and \( c = -18 \) into the formula:

\[
x = \frac{-1 \pm \sqrt{1^2 - 4(5)(-18)}}{2(5)}
\]

Let's calculate this.The solutions to the quadratic equation \( 5x^2 + x - 18 = 0 \) are:

\[
x_1 = 1.8 \quad \text{and} \quad x_2 = -2.0
\]

These are the values of \( x \) that satisfy the equation.

Would you like more details or have any questions? Here are 5 related questions:

1. How would you verify the solutions \( x_1 = 1.8 \) and \( x_2 = -2.0 \)?
2. Can the quadratic equation \( 5x^2 + x - 18 = 0 \) be factored instead of using the quadratic formula?
3. What are the key features of the graph of \( y = 5x^2 + x - 18 \)?
4. How does changing the coefficient \( a \) in \( 5x^2 + x - 18 \) affect the shape of the parabola?
5. What is the axis of symmetry of the parabola represented by \( y = 5x^2 + x - 18 \)?

**Tip:** When the discriminant (the part under the square root) is positive, the quadratic equation has two real solutions.

Learn how to solve the quadratic equation 5x² + x - 18 = 0 with a detailed step-by-step solution using the quadratic formula. This problem covers key algebraic concepts, including the quadratic formula and its application. Suitable for high school students in Grades 10-12.

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