Mr Daniels Maths
Solving Equations by Completing the Square

Set 1

Set 2

Set 3

Q1) \(x^2 -2x =0 \) [ \( x= 2 \) or \( x= 0 \)
]

Q1) \(x^2 + 8x+5 =0\) [ \(x=-4 ± \sqrt{11}\) ]

Q1) \(x^2 + 11x-5 =0\) [ \(x= \)-5\(\frac{1}{2}\) ± \( \sqrt{{ 35\frac{1}{4} }}\)]

Q2) \(x^2 -2x =0 \) [ \( x= 2 \) or \( x= 0 \)
]

Q2) \(x^2 + 16x-2 =0\) [ \(x=-8 ± \sqrt{66}\) ]

Q2) \(x^2 + 19x-7 =0\) [ \(x= \)-9\(\frac{1}{2}\) ± \( \sqrt{{ 97\frac{1}{4} }}\)]

Q3) \(x^2 -2x =0 \) [ \( x= 2 \) or \( x= 0 \)
]

Q3) \(x^2 + 16x-2 =0\) [ \(x=-8 ± \sqrt{66}\) ]

Q3) \(x^2 + 15x-9 =0\) [ \(x= \)-7\(\frac{1}{2}\) ± \( \sqrt{{ 65\frac{1}{4} }}\)]

Q4) \(x^2 + 4x =0 \) [ \( x= 0 \) or \( x= -4 \)
]

Q4) \(x^2 + 16x+6 =0\) [ \(x=-8 ± \sqrt{58}\) ]

Q4) \(x^2 + 7x-6 =0\) [ \(x= \)-3\(\frac{1}{2}\) ± \( \sqrt{{ 18\frac{1}{4} }}\)]

Q5) \(x^2 -2x =0 \) [ \( x= 2 \) or \( x= 0 \)
]

Q5) \(x^2 + 2x-9 =0\) [ \(x=-1 ± \sqrt{10}\) ]

Q5) \(x^2 + 5x-10 =0\) [ \(x= \)-2\(\frac{1}{2}\) ± \( \sqrt{{ 16\frac{1}{4} }}\)]

Q6) \(x^2 -6x =0 \) [ \( x= 6 \) or \( x= 0 \)
]

Q6) \(x^2 + 6x-8 =0\) [ \(x=-3 ± \sqrt{17}\) ]

Q6) \(x^2 + 7x-6 =0\) [ \(x= \)-3\(\frac{1}{2}\) ± \( \sqrt{{ 18\frac{1}{4} }}\)]

Q7) \(x^2 + 6x =0 \) [ \( x= 0 \) or \( x= -6 \)
]

Q7) \(x^2 + 6x-2 =0\) [ \(x=-3 ± \sqrt{11}\) ]

Q7) \(x^2 + 19x-8 =0\) [ \(x= \)-9\(\frac{1}{2}\) ± \( \sqrt{{ 98\frac{1}{4} }}\)]

Q8) \(x^2 -8x =0 \) [ \( x= 8 \) or \( x= 0 \)
]

Q8) \(x^2 + 8x+10 =0\) [ \(x=-4 ± \sqrt{6}\) ]

Q8) \(x^2 + 11x-3 =0\) [ \(x= \)-5\(\frac{1}{2}\) ± \( \sqrt{{ 33\frac{1}{4} }}\)]

Q9) \(x^2 + 2x =0 \) [ \( x= 0 \) or \( x= -2 \)
]

Q9) \(x^2 + 6x+5 =0\) [ \(x=-3 ± \sqrt{4}\) ]

Q9) \(x^2 + 17x-3 =0\) [ \(x= \)-8\(\frac{1}{2}\) ± \( \sqrt{{ 75\frac{1}{4} }}\)]

Q10) \(x^2 + 4x =0 \) [ \( x= 0 \) or \( x= -4 \)
]

Q10) \(x^2 + 10x+7 =0\) [ \(x=-5 ± \sqrt{18}\) ]

Q10) \(x^2 + 15x-4 =0\) [ \(x= \)-7\(\frac{1}{2}\) ± \( \sqrt{{ 60\frac{1}{4} }}\)]