Solving a quadratic by completing the square Revision Card

AI generatedAlgebraGCSE Higher

Include both square-root branches.

Put the quadratic equal to zero before factorising or using the quadratic formula.
Keep both square-root branches. Do not divide by an expression containing , as this can remove a root.
Give exact answers unless rounding is requested. In a context, reject only roots that are not permitted.

Example 1

Solve the quadratic equation. Give all real roots.

Halve the coefficient of

to get

. Add its square,

, to both sides.

Take both square roots. Include the positive and negative branches.

Example 2

Solve the quadratic equation. Give all real roots.

Halve the coefficient of

to get

. Add its square,

, to both sides.

Take both square roots. Include the positive and negative branches.

Your turn

Question 1

Solve the quadratic equation. Give all real roots.

Check answer

Halve the coefficient of

to get

. Add its square,

, to both sides.

Take both square roots. Include the positive and negative branches.

Question 2

Solve the quadratic equation. Give all real roots.

Check answer

Halve the coefficient of

to get

. Add its square,

, to both sides.

Take both square roots. Include the positive and negative branches.

Question 3

Solve the quadratic equation. Give all real roots.

Check answer

Halve the coefficient of

to get

. Add its square,

, to both sides.

Take both square roots. Include the positive and negative branches.

Question 4

Solve the quadratic equation. Give all real roots.

Check answer

Halve the coefficient of

to get

. Add its square,

, to both sides.

Take both square roots. Include the positive and negative branches.

Question 5

Solve the quadratic equation. Give all real roots.

Check answer

Halve the coefficient of

to get

. Add its square,

, to both sides.

Take both square roots. Include the positive and negative branches.