Questions: Use the quadratic formula to solve 5x^2 + 3x - 3 = 0 Round your answer to the nearest If there is more than one solution, x=

Solution Steps

To solve the quadratic equation \(5x^2 + 3x - 3 = 0\) using the quadratic formula, we identify the coefficients \(a = 5\), \(b = 3\), and \(c = -3\). The quadratic formula is given by:

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

We will calculate the discriminant \(b^2 - 4ac\) and then use it to find the two possible values for \(x\).

For the quadratic equation \(5x^2 + 3x - 3 = 0\), we identify the coefficients:

• \(a = 5\)
• \(b = 3\)
• \(c = -3\)

We calculate the discriminant using the formula \(D = b^2 - 4ac\): \[ D = 3^2 - 4 \cdot 5 \cdot (-3) = 9 + 60 = 69 \]

Using the quadratic formula \(x = \frac{{-b \pm \sqrt{D}}}{2a}\), we find the two solutions: \[ x_1 = \frac{{-3 + \sqrt{69}}}{10} \quad \text{and} \quad x_2 = \frac{{-3 - \sqrt{69}}}{10} \]

Calculating these values gives: \[ x_1 \approx 0.5307 \quad \text{and} \quad x_2 \approx -1.1307 \]

Rounding the solutions to the nearest integer: \[ x_1 \text{ rounded} = 1 \quad \text{and} \quad x_2 \text{ rounded} = -1 \]

Final Answer