Question

solve the quadratic equation: $9x^2 = 4 + 7x$

answer
$\frac{7pmsqrt{193}}{18}$ $\frac{-4pmsqrt{-236}}{18}$ $\frac{7pmsqrt{-95}}{18}$ $pm1$

Explanation:

Step1: Rewrite the equation

Rewrite \(9x^{2}=4 + 7x\) in standard quadratic form \(ax^{2}+bx + c = 0\). Subtract \(4\) and \(7x\) from both sides: \(9x^{2}-7x - 4=0\). Here, \(a = 9\), \(b=-7\), \(c = - 4\).

Step2: Apply the quadratic formula

The quadratic formula is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). Substitute \(a = 9\), \(b=-7\), \(c = - 4\) into the formula. First, calculate the discriminant \(D=b^{2}-4ac=(-7)^{2}-4\times9\times(-4)=49 + 144 = 193\). Then, \(x=\frac{-(-7)\pm\sqrt{193}}{2\times9}=\frac{7\pm\sqrt{193}}{18}\).

Answer:

\(\boldsymbol{\frac{7\pm\sqrt{193}}{18}}\) (the first option in the given choices)