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) \(x^2 + 8x+3 =0\) [ \(x=-4 ± \sqrt{13}\) ]

Q1) \(x^2 + 17x-4 =0\) [ \(x= \)-8\(\frac{1}{2}\) ± \( \sqrt{{ 76\frac{1}{4} }}\)]

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

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

Q2) \(x^2 + 11x-7 =0\) [ \(x= \)-5\(\frac{1}{2}\) ± \( \sqrt{{ 37\frac{1}{4} }}\)]

Q3) \(x^2 + 8x =0 \) [ \( x= 0 \) or \( x= -8 \)
]

Q3) \(x^2 + 4x-7 =0\) [ \(x=-2 ± \sqrt{11}\) ]

Q3) \(x^2 + 11x-2 =0\) [ \(x= \)-5\(\frac{1}{2}\) ± \( \sqrt{{ 32\frac{1}{4} }}\)]

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

Q4) \(x^2 + 10x-7 =0\) [ \(x=-5 ± \sqrt{32}\) ]

Q4) \(x^2 + 7x-10 =0\) [ \(x= \)-3\(\frac{1}{2}\) ± \( \sqrt{{ 22\frac{1}{4} }}\)]

Q5) \(x^2 -8x =0 \) [ \( x= 8 \) or \( x= 0 \)
]

Q5) \(x^2 + 4x-4 =0\) [ \(x=-2 ± \sqrt{8}\) ]

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

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

Q6) \(x^2 + 14x+2 =0\) [ \(x=-7 ± \sqrt{47}\) ]

Q6) \(x^2 + 11x-7 =0\) [ \(x= \)-5\(\frac{1}{2}\) ± \( \sqrt{{ 37\frac{1}{4} }}\)]

Q7) \(x^2 + 4x =0 \) [ \( x= 0 \) or \( x= -4 \)
]

Q7) \(x^2 + 8x-6 =0\) [ \(x=-4 ± \sqrt{22}\) ]

Q7) \(x^2 + 11x-9 =0\) [ \(x= \)-5\(\frac{1}{2}\) ± \( \sqrt{{ 39\frac{1}{4} }}\)]

Q8) \(x^2 + 10x =0 \) [ \( x= 0 \) or \( x= -10 \)
]

Q8) \(x^2 + 18x-9 =0\) [ \(x=-9 ± \sqrt{90}\) ]

Q8) \(x^2 + 15x-9 =0\) [ \(x= \)-7\(\frac{1}{2}\) ± \( \sqrt{{ 65\frac{1}{4} }}\)]

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

Q9) \(x^2 + 4x-8 =0\) [ \(x=-2 ± \sqrt{12}\) ]

Q9) \(x^2 + 15x-9 =0\) [ \(x= \)-7\(\frac{1}{2}\) ± \( \sqrt{{ 65\frac{1}{4} }}\)]

Q10) \(x^2 + 10x =0 \) [ \( x= 0 \) or \( x= -10 \)
]

Q10) \(x^2 + 12x+8 =0\) [ \(x=-6 ± \sqrt{28}\) ]

Q10) \(x^2 + 9x-6 =0\) [ \(x= \)-4\(\frac{1}{2}\) ± \( \sqrt{{ 26\frac{1}{4} }}\)]