Questions: Solve the equation. x(5x+9)=2

Solution Steps

To solve the quadratic equation \(x(5x + 9) = 2\), we first expand the equation to get it into standard quadratic form \(ax^2 + bx + c = 0\). Then, we can use the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\) to find the solutions for \(x\).

We start with the equation given in the problem: \[ x(5x + 9) = 2 \] Expanding this, we get: \[ 5x^2 + 9x - 2 = 0 \]

From the standard form \(ax^2 + bx + c = 0\), we identify the coefficients:

• \(a = 5\)
• \(b = 9\)
• \(c = -2\)

The discriminant \(D\) is calculated as follows: \[ D = b^2 - 4ac = 9^2 - 4 \cdot 5 \cdot (-2) = 81 + 40 = 121 \]

Using the quadratic formula: \[ x = \frac{-b \pm \sqrt{D}}{2a} \] we find the two solutions: \[ x_1 = \frac{-9 + \sqrt{121}}{2 \cdot 5} = \frac{-9 + 11}{10} = \frac{2}{10} = 0.2 \] \[ x_2 = \frac{-9 - \sqrt{121}}{2 \cdot 5} = \frac{-9 - 11}{10} = \frac{-20}{10} = -2.0 \]

Final Answer