Mr Daniels Maths
Solving Equations by Completing the Square

Set 1

Set 2

Set 3

Q1) \(x^2 + 10x =0 \) [ \( x= 0 \) or \( x= -10 \)
]

Q1) \(x^2 + 10x-9 =0\) [ \(x=-5 ± \sqrt{34}\) ]

Q1) \(x^2 + 15x-9 =0\) [ \(x= \)-7\(\frac{1}{2}\) ± \( \sqrt{{ 65\frac{1}{4} }}\)]

Q2) \(x^2 -6x =0 \) [ \( x= 6 \) or \( x= 0 \)
]

Q2) \(x^2 + 16x+10 =0\) [ \(x=-8 ± \sqrt{54}\) ]

Q2) \(x^2 + 11x-5 =0\) [ \(x= \)-5\(\frac{1}{2}\) ± \( \sqrt{{ 35\frac{1}{4} }}\)]

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

Q3) \(x^2 + 12x-4 =0\) [ \(x=-6 ± \sqrt{40}\) ]

Q3) \(x^2 + 19x-10 =0\) [ \(x= \)-9\(\frac{1}{2}\) ± \( \sqrt{{ 100\frac{1}{4} }}\)]

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

Q4) \(x^2 + 16x-6 =0\) [ \(x=-8 ± \sqrt{70}\) ]

Q4) \(x^2 + 9x-5 =0\) [ \(x= \)-4\(\frac{1}{2}\) ± \( \sqrt{{ 25\frac{1}{4} }}\)]

Q5) \(x^2 -4x =0 \) [ \( x= 4 \) or \( x= 0 \)
]

Q5) \(x^2 + 14x+4 =0\) [ \(x=-7 ± \sqrt{45}\) ]

Q5) \(x^2 + 11x-7 =0\) [ \(x= \)-5\(\frac{1}{2}\) ± \( \sqrt{{ 37\frac{1}{4} }}\)]

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

Q6) \(x^2 + 18x-6 =0\) [ \(x=-9 ± \sqrt{87}\) ]

Q6) \(x^2 + 17x-6 =0\) [ \(x= \)-8\(\frac{1}{2}\) ± \( \sqrt{{ 78\frac{1}{4} }}\)]

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

Q7) \(x^2 + 14x+5 =0\) [ \(x=-7 ± \sqrt{44}\) ]

Q7) \(x^2 + 13x-9 =0\) [ \(x= \)-6\(\frac{1}{2}\) ± \( \sqrt{{ 51\frac{1}{4} }}\)]

Q8) \(x^2 + 6x =0 \) [ \( x= 0 \) or \( x= -6 \)
]

Q8) \(x^2 + 10x+2 =0\) [ \(x=-5 ± \sqrt{23}\) ]

Q8) \(x^2 + 19x-2 =0\) [ \(x= \)-9\(\frac{1}{2}\) ± \( \sqrt{{ 92\frac{1}{4} }}\)]

Q9) \(x^2 + 4x =0 \) [ \( x= 0 \) or \( x= -4 \)
]

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

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

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

Q10) \(x^2 + 12x-2 =0\) [ \(x=-6 ± \sqrt{38}\) ]

Q10) \(x^2 + 9x-8 =0\) [ \(x= \)-4\(\frac{1}{2}\) ± \( \sqrt{{ 28\frac{1}{4} }}\)]