Find the values of x for the equation: x^2 - 8x = 105

When presented with an equation that involves x^2, it is likely to be a quadratic equation. This leads us to rearrange to the equation above into the form of ax^2 + b + c = 0. Therefore the equation can be rearranged into x^2 - 8x - 105 = 0.

There are two main methods to solve this quadratic equation - factorising and quadratic formula.

Factorising involves finding two numbers that can multiply together to give -105 and add to form -8. As both numbers are negative we can deduce that one of those numbers are negative and the other is positive.

First start by stating the factors of 105: 1, 3, 5, 7 & 15. Using these numbers, find a pair that would give you a difference of 8. This is 7 and 15. There are two equations that we could form from this:

- (x+7)(x-15)=0

- (x-7)(x+15)=0

Only the first quadratic equation gives rise to -8x and therefore is the correct equation. The values of x is then -7 & 15 as you take the number within the bracket and inverse the sign.

The alternative method is using the quadratic formula: x = (-b +/- SQRT(b^2 - 4ac))/2a. The values for a = 1, b = -8 & c = -105. By substituting the values into the equation we get the answers -7 & 15.

Answered by Dhulaxy M. Maths tutor

5178 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve for x and y, with x and y satisfying the equations x+4y=5 and 2x+2y=16.


Solve for x and y: 2x +5y + 5= 0 , 2y + 31= 5x


Given a spinner divided in 3 sections numbered 1, 2 and 3, and that the arc of section 2 is double that of section one (~57.6 cm), calculate pi to 2 decimal places. The radius of the spinner is 30cm and the angle sub-intended by section 3 is 30 degrees.


3kg of meat costs £54, Nina buys 2 kg of the meat. Work out how much Nina pays. (non-calculator)


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences