If x^2 = 16, why isn't the answer just x = 4?

You're right that x = 4 is a solution to the equation - but the problem is it's not the only solution, x = -4 also works.You have to be careful not to take a shortcut by simply taking the square root of both sides of the equation, because the square root of 16 is plus or minus 4. Forgetting to include "plus or minus" every time you square root an equation is a very easy mistake to make, but luckily there's another method for solving this equation...Move all the terms in the equation to one side of the equals sign;x^2 - 16 = 0Because the left hand side is a "difference of two squares" it can easily be factorised;(x - 4)(x + 4) = 0So, x - 4 = 0 or x + 4 = 0.Therefore x = 4 or x = -4.This is the normal way we solve quadratic equations, and it means we are much less likely to make a silly mistake!

LD
Answered by Laurie D. β€’ Maths tutor

13316 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers β–Έ

There are only 7 blue pens, 4 green pens and 6 red pens in a box. One pen is taken at random from the box. Write down the probability that this pen is blue.


Solve 5w – 3 = 3w + 15


Given: 𝑓(π‘₯) = π‘Žπ‘₯^3 + 𝑏π‘₯^2 βˆ’ 3 and 𝑓"(βˆ’2) = 0. If it is further given that the point (βˆ’3; 6) lies on the graph of 𝑓. Show that π‘Ž = 1/3 and 𝑏 = 2.


A triangle has 3 angles of 60 degrees, (5y-40) degrees, and (2y+20) degrees. Show that the triangle is equilateral.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

Β© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences