Quadratic Equation

A Quadratic equation is any equation that has this kind of algebraic format $a{x}^2+\mathrm{bx}+\mathrm{c}=0$

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How to solve a quadratic equation using the quadratic formula

Solve the following quadratic equation using the quadratic formula

$4x^2-\mathrm{4x}-24=0$

Quadratic Format

$a{x}^2+\mathrm{bx}+\mathrm{c}=0$

Quadratic Formula

x = $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

a = 4, b = -4, c = -24

Solution:

x = $\frac{-\mathrm{(-4)}\pm \sqrt{{\mathrm{-4}}^2-4\mathrm{\times 4}\mathrm{\times -24}}}{2\mathrm{\times 4}}$

x = $\frac{-\mathrm{(-4)}\pm \sqrt{\mathrm{16}-\mathrm{(-384)}}}{8}$

x = $\frac{-\mathrm{(-4)}\pm \sqrt{\mathrm{16}+\mathrm{384}}}{8}$

x = $\frac{-\mathrm{(-4)}\pm \sqrt{\mathrm{400}}}{8}$

x = $\frac{4\pm \mathrm{20}}{8}$

x = $\frac{4+\mathrm{20}}{8}$ and x = $\frac{4-\mathrm{20}}{8}$

x = 3, and x = -2

How to Solve the Quadratic equation example

Solve the equation

$5x^2-\mathrm{2x}-1=0$

a = 5, b = -2, c = -1

Solution:

x = $\frac{-\mathrm{(-2)}\pm \sqrt{{\mathrm{(-2)}}^2-4\mathrm{\times 5}\mathrm{\times -1}}}{2\mathrm{\times 5}}$

x = $\frac{2\pm \sqrt{4-\mathrm{(-20)}}}{10}$

x = $\frac{2\pm \sqrt{4+20}}{10}$

x = $\frac{2\pm \sqrt{\mathrm{24}}}{10}$

x = $\frac{2\pm \mathrm{4.899}}{10}$

x = $\frac{2+\mathrm{4.899}}{10}$ and $\frac{2-\mathrm{4.899}}{10}$

Answer: x = 0.69 and x = -0.29

Quadratic Formula

Factorising Quadratic Equation

Complete the Square