Completing the square is the process of rearranging an expression of the form ax^2 + bx + c into an equivalent expression of the form a(x + p)^2 + q

Solving quadratic equations by completing the square

Maths

In this unit, pupils learnt to solve quadratic equations by factorising and this skill will be required in the future unit through manipulating two simultaneous equations to find the solutions. For pupils studying the higher content, solving quadratic equations is required if one of the simultaneous equations is a quadratic.

In the prior unit, pupils used the distributive law to find the product of two binomials. In algebraic manipulation, pupils use apply this knowledge in order to factorise quadratics.

Algebraic manipulation

Write $$x^2 + 4x + 5$$ in the form of $$(x + p)^2 + q$$

Express $$x^2 + 6x + 10$$ as $$(x + p)^2 + q$$

Express $$x^2 + 8x + 14$$ as $$(x + p)^2 + q$$

Put $$x^2 - 4x + 5$$ in the form $$(x + p)^2 + q$$

Solve by completing the square: $$x^2 + 6x + 8 = 0$$

Solve by completing the square: $$x^2 + 6x + 5 = 0$$

Which of these is a solution for $$(x - 3)^2 = 0$$?

Which of these is a solution for $$x^2 = 0$$?

Which of these is a solution for $$(x - 4)(x + 2) = 0$$?

The equation for this curve is $$y=x^2 + 3x + 3$$. How many real solutions will it have? 

Rearrange the following equation to make $$m$$ the subject: $$3x - m = 9$$

Rearrange the following equation to make $$x$$ the subject: $$3x - m = 9$$

This lesson will be removed by end of Summer Term 2025.

Solving quadratic equations by completing the square

Lesson outcome

This lesson will be removed by end of Summer Term 2025.