Solve the following equations by factorising: 1) 7a + a² - 18 = 0 , 2) c² + 2c = 35

Question

explanation and working out please.

Answer 1

One way to solve quadratic equations is to set them equal to zero, factor them, and solve.  This works because the only way to get zero when you multiply two things together is if one or the other of those things are zero.

You first job is to get them in the right order.

ax² +bx + c = 0

So in your first problem, you have to re-arrange the terms, so it is the squared term, then the term to the first power, then the constant.

a² +7a -18 = 0

(a +9) (a -2) = 0

Set the factors to 0 and solve.

 

In your second problem, you have to subtract the 35 from each side, so it is equal to zero.  Then you factor, and set each factor to zero, then solve.  

 

You can do it!

 

 

Answer 2

It helps to first put the equations in standard form.

 

(1)

 

a² + 7a - 18 = 0

 

(a + A)(a + B) = 0

 

Find 2 numbers A and B such that AB = -18 (the constant term) and A+B = 7 (the coefficient of the linear term).  Usually, just guess.  Note that 9 and -2 work.

 

(a + 9)(a - 2) = 0

 

Test this answer.

 

(2)

 

c² + 2c - 35 = 0

 

Note that 7 and -5 work.

 

(c + 7)(c - 5) = 0

 

Test this answer.