Equations

Ontario 10 Applied (MFM2P)

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.

**Solve**, $x^2-36=0$`x`2−36=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**

$x^2-36=0$`x`2−36=0

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

$x^2=36$`x`2=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

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

Solve for $k$`k`: $-3k^2=-75$−3`k`2=−75

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