Solving Quadratic Equations Using Square Roots

The equation can be solved by taking square roots on both sides. Remember that to ensure we find all potential solutions, we need to consider both the principal root and the negative root!

Therefore, the equation has two real solutions. These solutions are x=8 and x=-8.

This time we need to isolate the x^2-term before taking square roots on both sides. Once again, if we do not want to miss any solution, we need to consider both the principal root and the negative root.

Therefore, the equation has two real solutions. These solutions are x=3 and x=-3.

Equation	Rewrite as $x^{2} = d$	Value of $d$	Number of Real Solutions
$- 4 x^{2} + 5 = 5$	$x^{2} = 0$	$d = 0$	One
$5 x^{2} - 125 = 0$	$x^{2} = 25$	$d = 25 \Rightarrow d > 0$	Two
$- 3 x^{2} - 27 = 0$	$x^{2} = - 9$	$d = - 9 \Rightarrow d < 0$	Zero

Equation	Rewrite
$- x^{2} + 4 = 0$	$- 1 (x - 0)^{2} + 4 = 0$
$3 x^{2} - 6 x + 5 = 0$	$3 (x - 1)^{2} + 2 = 0$
$5 x^{2} = 3 x + 1$	$5 (x - \frac{3}{1 0})^{2} + (- \frac{2 9}{2 0}) = 0$
$4 x^{2} + 4 x = - 2$	$4 (x - (- \frac{1}{2}))^{2} + 1 = 0$
$4 x^{2} + 4 x = - 2$	$4 (x - (- \frac{1}{2}))^{2} + 1 = 0$
$10 x^{2} + 160 = 80 x$	$10 (x - 4)^{2} + 0 = 0$

Solving Quadratic Equations Using Square Roots

Catch-Up and Review

Determining the Number of Solutions

Simple Quadratic Equations

Number of Solutions of a Simple Quadratic Equation

Proof

$d > 0$

$d = 0$

$d < 0$

Number of Solutions

Hint

Solution

How Many Solutions?

Solving Quadratic Equations with Square Roots

Rational Solutions

Hint

Solution

Irrational Solutions

Hint

Solution

Solving Simple Quadratic Equations

Solving Other Type of Quadratic Equation

Hint

Solution

A Process Called Completing the Square