Mr Daniels Maths
Solving Equations by Completing the Square

Set 1

Set 2

Set 3

Q1) \(x^2 -6x =0 \) [ \( x= 6 \) or \( x= 0 \)
]

Q1) \(x^2 + 16x-7 =0\) [ \(x=-8 ± \sqrt{71}\) ]

Q1) \(x^2 + 11x-4 =0\) [ \(x= \)-5\(\frac{1}{2}\) ± \( \sqrt{{ 34\frac{1}{4} }}\)]

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

Q2) \(x^2 + 6x-4 =0\) [ \(x=-3 ± \sqrt{13}\) ]

Q2) \(x^2 + 7x-6 =0\) [ \(x= \)-3\(\frac{1}{2}\) ± \( \sqrt{{ 18\frac{1}{4} }}\)]

Q3) \(x^2 + 6x =0 \) [ \( x= 0 \) or \( x= -6 \)
]

Q3) \(x^2 + 10x-6 =0\) [ \(x=-5 ± \sqrt{31}\) ]

Q3) \(x^2 + 9x-4 =0\) [ \(x= \)-4\(\frac{1}{2}\) ± \( \sqrt{{ 24\frac{1}{4} }}\)]

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

Q4) \(x^2 + 14x+8 =0\) [ \(x=-7 ± \sqrt{41}\) ]

Q4) \(x^2 + 11x-3 =0\) [ \(x= \)-5\(\frac{1}{2}\) ± \( \sqrt{{ 33\frac{1}{4} }}\)]

Q5) \(x^2 + 10x =0 \) [ \( x= 0 \) or \( x= -10 \)
]

Q5) \(x^2 + 14x+2 =0\) [ \(x=-7 ± \sqrt{47}\) ]

Q5) \(x^2 + 11x-10 =0\) [ \(x= \)-5\(\frac{1}{2}\) ± \( \sqrt{{ 40\frac{1}{4} }}\)]

Q6) \(x^2 -10x =0 \) [ \( x= 10 \) or \( x= 0 \)
]

Q6) \(x^2 + 10x+6 =0\) [ \(x=-5 ± \sqrt{19}\) ]

Q6) \(x^2 + 15x-7 =0\) [ \(x= \)-7\(\frac{1}{2}\) ± \( \sqrt{{ 63\frac{1}{4} }}\)]

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

Q7) \(x^2 + 8x-7 =0\) [ \(x=-4 ± \sqrt{23}\) ]

Q7) \(x^2 + 3x-6 =0\) [ \(x= \)-1\(\frac{1}{2}\) ± \( \sqrt{{ 8\frac{1}{4} }}\)]

Q8) \(x^2 -4x =0 \) [ \( x= 4 \) or \( x= 0 \)
]

Q8) \(x^2 + 8x+4 =0\) [ \(x=-4 ± \sqrt{12}\) ]

Q8) \(x^2 + 9x-10 =0\) [ \(x= \)-4\(\frac{1}{2}\) ± \( \sqrt{{ 30\frac{1}{4} }}\)]

Q9) \(x^2 + 8x =0 \) [ \( x= 0 \) or \( x= -8 \)
]

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

Q9) \(x^2 + 5x-4 =0\) [ \(x= \)-2\(\frac{1}{2}\) ± \( \sqrt{{ 10\frac{1}{4} }}\)]

Q10) \(x^2 -8x =0 \) [ \( x= 8 \) or \( x= 0 \)
]

Q10) \(x^2 + 10x+2 =0\) [ \(x=-5 ± \sqrt{23}\) ]

Q10) \(x^2 + 13x-8 =0\) [ \(x= \)-6\(\frac{1}{2}\) ± \( \sqrt{{ 50\frac{1}{4} }}\)]