GCSE Maths (AQA)

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Solving by Completing the Square

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Algebra Solving Equations and Inequalities

Solving by Completing the Square

5:34 More Quadratic Equations
Spec A18
Previous The Quadratic Formula Next Approximating Solutions with Graphs
  • Quadratic equations can be solved by completing the square
  • To make x the subject, we add or subtract the necessary values to isolate x
  • Taking the square root of both sides gives us the possible solutions for x
  • If the equation has no solutions, it is because we are trying to take the square root of a negative number
  • The completed square formula is x^2 + bx + c = (x + b/2)^2 - (b/2)^2 + c
  • We can simplify the equation by combining like terms
  • The constant term is separated from the squared bracket by moving it to the other side of the equal sign
  • Taking the square root of both sides gives us the possible solutions for x
  • To make x the subject, we group the constants on the other side of the equal sign
  • The solutions can be written in the form p + root q, where p and q are integers to be found

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