Thread: How to solve this equation by completing the square

Hello

I can solve this question by using the quadratic formula but want to see how to solve by completing the square.

Equation is

So my working is:









But how do I get rid of the . And is the above correct so far.

My problem is that multiplying both sides by -5 means number on rhs will be negative and so no solution. But I know the curve does cross the x axis - so there is a solution. Can anyone show me the final steps to solve this using completing the square?

Angus

You can multiply both sides by -5, yielding x^2 - 10x + \frac{45}{2} = 0. Then:

x^2 - 10x + 25 + \frac{45}(2} = 25

(x - 5)^2 = 25 - \frac{45}{2}

(x - 5)^2 = \frac{5}{2}

(Sorry, my LaTex isn't compiling)

When you add the 25 within the parentheses, you are really subtracting 5 because of the coefficient of -1/5, so you need to add 5 outside.

What you have done is subtract 30 from the left side, while leaving the right side unchanged. You are correct up to:



Your next step should be:



Can you finish from there?

Originally Posted by angypangy

Hello

I can solve this question by using the quadratic formula but want to see how to solve by completing the square.

Equation is

So my working is:









But how do I get rid of the . And is the above correct so far.

My problem is that multiplying both sides by -5 means number on rhs will be negative and so no solution. But I know the curve does cross the x axis - so there is a solution. Can anyone show me the final steps to solve this using completing the square?

Angus

It's easier to multiply through by -5 initially to clear that fraction.









This should now give two real solution

Originally Posted by e^(i*pi)

It's easier to multiply through by -5 initially to clear that fraction.









This should now give two real solution

Ah, yes that is easier. thanks.