Tag Archives: Equation

Solving Quadratic Equations by Quadratic Formula

Solving Quadratic Equations by Quadratic Formula

In many cases, factorising a quadratic equation or completing the square can be long or difficult. We can instead use the quadratic formula. \( \begin{align} \displaystyle \require{AMSsymbols} \require{color}ax^2 + bx + c &= 0 \\ax^2 + bx &= -c \\x^2 + \dfrac{b}{a}x &= -\dfrac{c}{a} \\x^2 + \dfrac{b}{a}x \color{red} + \Big(\dfrac{b}{2a}\Big)^2 &= -\dfrac{c}{a} \color{red} + \Big(\dfrac{b}{2a}\Big)^2\\\Big(x+\dfrac{b}{2a}\Big)^2 […]

The Golden Ratio

The Golden Ratio

Since the days of old, artists, as well as mathematicians, have known that there is a special, aesthetically pleasing rectangle with width $1$, length $x$, and the following property:When a square of side $1$ is removed, the remaining rectangle has the same proportions as the original rectangle. Since the new rectangle has a width $x-1$ […]

Surd Equations Reducible to Quadratics

Surd Equations Reducible to Quadratics

Surd Equations Reducible to Quadratic for Math Algebra is done squaring both sides for removing surds and radical expressions. Make sure to check whether the solutions are correct by substituting them into the original surd equations. Question 1 Solve \( x = \sqrt{x+2} \). \( \begin{aligned} \displaystyle \require{AMSsymbols} \require{color}x^2 &= x+2 &\color{red} \text{square both sides} […]