Question

Quiz: Completing the Square 7:Solving Quadratic Equations

Answer 1

Answer:

(x + 2)(2x + 2) = 110; x = 5.93 mf2

Step-by-step explanation:

mf2

Answer 2

Answer:

5.93m

Step-by-step explanation:

I don't know what's happening exactly in a) but I solved b) by completing the square for you. See the attached image for my exact working.

Firstly I expanded the quadratic and then rearranged to get the equation

x^2 + 3x = 53

Then I halved the multiplier of the middle term and added the square of the result to both sides. I.e. I added 1.5^2 to both sides of the equation.

Then i factorised the left side of the equation into a perfect square (x+1.5)^2. This can be mentally checked by using the "SAM" method. 1.5+1.5=3, which is the middle term of the expanded equation, and 1.5×1.5 = 1.5^2 = 2.25.

So we have the equation (x+1.5)^2 = 55.25

Next square root both sides and do some rearranging to get x = 5.93

Hope this helps ☺️

Side note: Theoretically, -7.433 is also the square root of 55.25, but using this value would result in a negative answer. As this question appears to be about areas and areas can't be negative, I'd keep away from using -7.433 and just stick to 7.433.