Step 1

Approach:

Quadratic Formula: For a quadratic equation \(ax^{2}+bx+c=0,\) where \(a\neq0,\)

the solutions are \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\)

Step 2

Calculation:

Given: \(x^{2}-0.011x-0.064=0.\)

Here, \(a=1,\ b=-0.011\) and \(c=-0.064\)

Substitute these values in quadratic formula.

\(x=\frac{-(-0.011)\pm\sqrt{(-0.011)^{2}-4(1)(-0.064)}}{2(1)}\)

\(=\frac{0.011\pm\sqrt{0.000121+0.256}}{2}\)

\(=\frac{0.011\pm\sqrt{0.256121}}{2}\)

Let us find the values of x using calculator.

\(x=\frac{0.011+\sqrt{0.256121}}{2}=\frac{0.517084}{2}=0.2585\)

\(x=\frac{0.011-\sqrt{0.256121}}{2}=\frac{-0.495084}{2}=-0.2475\)

Rounding to three decimals, the solutions are \(x=-0.284,\ x=0.259\)