Quadratic Equation One Unknown

Overview

Engineering reference data for Quadratic Equation One Unknown in miscellaneous.

Key Formulas

Unit Conversion

$y = x \cdot k$

Multiply by conversion factor.

Linear Interpolation

$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$

Estimate between two known points.

Percentage

$p = \frac{\text{part}}{\text{whole}} \times 100\%$

Part as fraction of whole.

Variables

Example Calculation

The following demonstrates solving a quadratic equation for specific coefficients.

Given:
$a = 1, \quad b = 6, \quad c = 5$

Step 1: Substitute into the quadratic formula.
$x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Step 2: Compute the values.
For the first root:
$x_1 = \frac{-6 + \sqrt{6^2 - 4 \cdot 1 \cdot 5}}{2 \cdot 1} = \frac{-6 + \sqrt{16}}{2} = \frac{-6 + 4}{2} = -1$

For the second root:
$x_2 = \frac{-6 - \sqrt{6^2 - 4 \cdot 1 \cdot 5}}{2 \cdot 1} = \frac{-6 - \sqrt{16}}{2} = \frac{-6 - 4}{2} = -5$

Result:
The solutions to the equation $x^2 + 6x + 5 = 0$ are $x_1 = -1$ and $x_2 = -5$.

References

• Original Source