Question

Solve for x using the quadratic formula.3x^2 +10x+8=3

Answer 1

The quadartic equation is 3x^2+10x+8=3.

Simplify the quadratic equation to obtain the equation in standard form ax^2+bx+c=0.

`\begin{gathered} 3x^2+10x+8=3 \\ 3x^2+10x+5=0 \end{gathered}`

The coefficent of x^2 is a=3, coefficient of x is b=10 and constant term is c=5.

The quadartic formula for the values of x is,

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

Substitute the values in the formula to obtain the value of x.

`\begin{gathered} x=\frac{-10\pm\sqrt[]{(10)^2-4\cdot3\cdot5}}{2\cdot3} \\ =\frac{-10\pm\sqrt[]{100-60}}{6} \\ =\frac{-10\pm\sqrt[]{40}}{6} \\ =\frac{-10\pm2\sqrt[]{10}}{6} \\ =\frac{-5\pm\sqrt[]{10}}{3} \end{gathered}`

The value of x is,

`\frac{-5\pm\sqrt[]{10}}{3}`