Questions: (4x-7)/2 = x^2 + 2x

Solution Steps

Multiply both sides of the equation \(\frac{4x-7}{2} = x^{2} + 2x\) by 2 to eliminate the fraction: \[ 4x - 7 = 2x^{2} + 4x \]

Rearrange the equation to bring all terms to one side: \[ 0 = 2x^{2} + 4x - 4x + 7 \] This simplifies to: \[ 0 = 2x^{2} + 7 \]

Rearranging gives us the standard form of the quadratic equation: \[ 2x^{2} + 7 = 0 \] To solve for \(x\), we can use the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\) where \(a = 2\), \(b = 0\), and \(c = 7\). This results in: \[ x = \frac{-0 \pm \sqrt{0^2 - 4 \cdot 2 \cdot 7}}{2 \cdot 2} = \frac{\pm \sqrt{-56}}{4} = \frac{\pm \sqrt{56}i}{4} = \frac{\pm \sqrt{14}i}{2} \]

Final Answer