New Zealand
Level 7 - NCEA Level 2

# Variable substitution method

## Interactive practice questions

We want to solve the following equation for $x$x: $x^4-34x^2+225=0$x434x2+225=0.

a

What substitution can we make to reduce this equation to a quadratic in the variable $p$p?

b

Substitute $p=x^2$p=x2 into the equation and solve for $p$p.

c

Now solve for $x$x using your previous answer as a reference. Write all solutions on the same line, separated by a comma.

Easy
Approx 4 minutes

We want to solve the following equation for $x$x: $25x^4-65x^2+36=0$25x465x2+36=0.

Consider the equation $81x^4-117x^2+36=0$81x4117x2+36=0.

Consider the equation $\left(4x+8\right)^2+16\left(4x+8\right)+48=0$(4x+8)2+16(4x+8)+48=0.

### Outcomes

#### M7-6

Manipulate rational, exponential, and logarithmic algebraic expressions

#### 91261

Apply algebraic methods in solving problems