# Solve quadratic equations (ax^2 = b)

Lesson

Solving basic or simple quadratics involves using algebraic manipulation, the easiest way to see these is to look at a few examples.

#### Examples

##### Question 1

Solve, $x^2-36=0$x236=0

Think: Identify the order of operations necessary to isolate the $x$x variable.  In this case we will deal with the subtraction then the square in that order.

Do

$x^2-36=0$x236=0

1) Use inverse operations to remove the$-36$36 from the LHS. The opposite of a $-36$36 is a $+$+$36$36

$x^2=36$x2=36

2) Use inverse operations to remove the square from the left hand side. The opposite of a square operation is a square root operation.

$x=6$x=6 or $x=-6$x=6

Remember that all square roots can have a positive or negative answer.  The solution for $x$x can also be written as $x=\pm6$x=±6.

Just to remind you, What is $4^2$42 and what is $\left(-4\right)^2$(4)2?   Hence $\sqrt{16}=\pm4$16=±4

##### Question 2

Solve for $y$y: $3y^2=75$3y2=75

#### Question 3

Solve for $k$k: $-3k^2=-75$3k2=75

### Outcomes

#### 10P.LR1.01

Solve first-degree equations involving one variable, including equations with fractional coefficients