Question

solve the quadratic equation using the quadratic formula. Then solve the equation using another method. which method do you prefer? explain.

Answer 1

Given:

The quadratic equation is,

$5x^2+38=3$

Explanation:

Simplify the equation.

$\begin{gathered} 5x^2+38-3=0 \\ 5x^2+0\cdot x+35=0 \end{gathered}$

For the given equation a = 5, b = 0 and c = 35.

The quadratic formula is,

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

Substitute the values in the equation to solve the equation.

$\begin{gathered} x=\frac{-0\pm\sqrt[]{(0)^2-4\cdot5\cdot35}}{2\cdot5} \\ =\frac{\pm\sqrt[]{-700}}{10} \\ =\frac{\pm10\sqrt[]{7}i}{10} \\ =\pm\sqrt{7}i \end{gathered}$

Second method:

Solve the equation.

$\begin{gathered} 5x^2+38=3 \\ 5x^2=3-38 \\ x^2=-\frac{35}{5} \\ x=\pm\sqrt[]{-7} \\ =\pm\sqrt[]{7}i \end{gathered}$

I prefer the second method for solving as quadratic equation donot have x terms, so it can be solved easily by combining the like terms.

If equation has x terms also and cannot split the middle terms then quadratic formula method is preffered.

Answer:

$\pm\sqrt[]{7}i$

Prefer second method as there are no x terms in quadratic equation, so it can be simplify easily by conbining like terms.