ANSWER
[tex]x\text{ = }\frac{-1.45\text{ - 0.847i}}{12}\text{ or }\frac{-1.45\text{ + 0.847i}}{12}[/tex]STEP-BY-STEP EXPLANATION
The equation of a chemical equilibrium reaction is given below as
[tex]Kc\text{ = }\frac{0.04-0.4x+x^2}{0.0225+0.15x+x^2}[/tex]Recall that, Kc = 7
The next step is to substitute the value of Kc = 7 into the above equation
[tex]7\text{ = }\frac{0.04-0.4x+x^2}{0.0225+0.15x+x^2}[/tex]The next step is to cross multiply
[tex]\begin{gathered} 0.04-0.4x+x^2\text{ = }7\cdot(0.0225+0.15x+x^2) \\ \text{open the parentheses} \\ 0.04-0.4x+x^2\text{ = }7\cdot\text{ }0.0225\text{ + 7 }\cdot\text{ 0.15x + 7 }\cdot x^2 \\ 0.04-0.4x+x^2\text{ = }0.1575+1.05x+7x^2 \\ \text{Collect the like terms} \\ x^2-7x^2\text{ - 0.4x - 1.05x + 0.04 - 0.1575 = 0} \\ -6x^2\text{ -1.45x - }0.1175\text{ = 0} \\ \end{gathered}[/tex]The next step is to solve for x in the equation using the general quadratic formula
Recall that,
[tex]ax^2\text{ + bx + c = 0}[/tex]Relating the two equations together, then, we have the following
a = -6
b = -1.45
c = -0.1175
[tex]\begin{gathered} x\text{ = }\frac{-b\text{ }\pm\sqrt[]{b^2\text{ - 4ac}}}{2a} \\ x\text{ = }\frac{-(-1.45)\text{ }\pm\sqrt[]{-1.45^2\text{ - (4 }\cdot-\text{ 6 }\cdot\text{ -0.1175)}}}{2\cdot\text{ -6}} \\ x\text{ = }\frac{1.45\text{ }\pm\sqrt[]{2.1025\text{ - }(2.82)}}{-12} \\ x\text{ = }\frac{\text{ 1.45 }\pm\sqrt[]{-0.7175}}{-12} \\ x\text{ = }\frac{1.45\pm\sqrt[]{0.7175}\text{ }\sqrt[]{-1}}{-12} \\ \text{ recall that, }\sqrt[]{-1\text{ }}\text{ = i} \\ x\text{ = }\frac{1.45\pm\sqrt[]{0.7175}\text{ i}}{-12} \\ x\text{ = }\frac{1.45\text{ }\pm0.847i}{-12} \\ x\text{ = }\frac{1.45\text{ + 0.847i}}{-12}\text{ or }\frac{1.45-\text{ 0.847i}}{-12} \\ x\text{ = }\frac{-1.45\text{ - 0.847i}}{12}\text{ or }\frac{-1.45\text{ + 0.847i}}{12} \end{gathered}[/tex]