Explained: "To solve: The equation x2−0.011x−0.064=0 using quadratic formula..."

ddaeeric

Answered question

2021-05-22

To solve:
The equation

x^{2} - 0.011 x - 0.064 = 0

using quadratic formula and a calculator, rounding to three decimals.

Answer & Explanation

Layton

Skilled2021-05-23Added 89 answers

Step 1
Approach:
Quadratic Formula: For a quadratic equation $a x^{2} + b x + c = 0,$ where $a \neq 0,$
the solutions are $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
Step 2
Calculation:
Given: $x^{2} - 0.011 x - 0.064 = 0.$
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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