Question

To solve: The equation x^{2}-0.011x-0.064=0 using quadratic formula and a calculator, rounding to three decimals.

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asked 2021-05-22
To solve:
The equation \(x^{2}-0.011x-0.064=0\) using quadratic formula and a calculator, rounding to three decimals.

Answers (1)

2021-05-23

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 \(x=-0.284,\ x=0.259\)

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