Michele Conway, Belle Cottingham, Alastair Duncombe and, Amanda George Solutions for Exercise 3: Exercise 1

Use trial and improvement method to solve the equation to one decimal place.

$x\left(x+4\right)=9$

Use trial and improvement method to solve the equation to one decimal place.

$5x\left(x+2\right)=19$

Use trial and improvement method to solve the equation to one decimal place.

$x\left(x^2+2\right)=4$

The table shows the values of $x^2-3x$. Use the table to find a solution to each of the equation $x^2-3x=20$. Give answer correct to $1$ decimal place.

The table shows the values of $x^2-3x$. Use the table to find a solution to each of the equation $x^2-3x=22$. Give answer correct to $1$ decimal place.

The table shows the values of $x^2-3x$. Use the table to find a solution to each of the equation $x^2=3x+24$. Give answer correct to $1$ decimal place.

John uses trial and improvement to solve the equation $3x^2+2x=90$ to $2$ decimal places. He uses $5.3$ as his starting point but the values seem to get further and further away from $90$. Identify the mistake that John makes. Use trial and improvement to finds the correct answer.

The shaded area in the shape below is $100 c{m}^2$. Use trial and improvement to calculate the side length of the square to $1$ decimal place.