Mr Daniels Maths
Solving Equations by Completing the Square

Set 1

Set 2

Set 3

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

Q1) \(x^2 + 16x-9 =0\) [ \(x=-8 ± \sqrt{73}\) ]

Q1) \(x^2 + 11x-6 =0\) [ \(x= \)-5\(\frac{1}{2}\) ± \( \sqrt{{ 36\frac{1}{4} }}\)]

Q2) \(x^2 + 4x =0 \) [ \( x= 0 \) or \( x= -4 \)
]

Q2) \(x^2 + 8x+2 =0\) [ \(x=-4 ± \sqrt{14}\) ]

Q2) \(x^2 + 11x-10 =0\) [ \(x= \)-5\(\frac{1}{2}\) ± \( \sqrt{{ 40\frac{1}{4} }}\)]

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

Q3) \(x^2 + 12x+7 =0\) [ \(x=-6 ± \sqrt{29}\) ]

Q3) \(x^2 + 7x-6 =0\) [ \(x= \)-3\(\frac{1}{2}\) ± \( \sqrt{{ 18\frac{1}{4} }}\)]

Q4) \(x^2 + 10x =0 \) [ \( x= 0 \) or \( x= -10 \)
]

Q4) \(x^2 + 8x-6 =0\) [ \(x=-4 ± \sqrt{22}\) ]

Q4) \(x^2 + 19x-6 =0\) [ \(x= \)-9\(\frac{1}{2}\) ± \( \sqrt{{ 96\frac{1}{4} }}\)]

Q5) \(x^2 -6x =0 \) [ \( x= 6 \) or \( x= 0 \)
]

Q5) \(x^2 + 6x+3 =0\) [ \(x=-3 ± \sqrt{6}\) ]

Q5) \(x^2 + 13x-4 =0\) [ \(x= \)-6\(\frac{1}{2}\) ± \( \sqrt{{ 46\frac{1}{4} }}\)]

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

Q6) \(x^2 + 10x-4 =0\) [ \(x=-5 ± \sqrt{29}\) ]

Q6) \(x^2 + 15x-2 =0\) [ \(x= \)-7\(\frac{1}{2}\) ± \( \sqrt{{ 58\frac{1}{4} }}\)]

Q7) \(x^2 + 8x =0 \) [ \( x= 0 \) or \( x= -8 \)
]

Q7) \(x^2 + 6x-7 =0\) [ \(x=-3 ± \sqrt{16}\) ]

Q7) \(x^2 + 5x-9 =0\) [ \(x= \)-2\(\frac{1}{2}\) ± \( \sqrt{{ 15\frac{1}{4} }}\)]

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

Q8) \(x^2 + 12x-9 =0\) [ \(x=-6 ± \sqrt{45}\) ]

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

Q9) \(x^2 -10x =0 \) [ \( x= 10 \) or \( x= 0 \)
]

Q9) \(x^2 + 12x-5 =0\) [ \(x=-6 ± \sqrt{41}\) ]

Q9) \(x^2 + 7x-3 =0\) [ \(x= \)-3\(\frac{1}{2}\) ± \( \sqrt{{ 15\frac{1}{4} }}\)]

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

Q10) \(x^2 + 10x+9 =0\) [ \(x=-5 ± \sqrt{16}\) ]

Q10) \(x^2 + 11x-3 =0\) [ \(x= \)-5\(\frac{1}{2}\) ± \( \sqrt{{ 33\frac{1}{4} }}\)]