Mr Daniels Maths
Solving Equations by Completing the Square

Set 1

Set 2

Set 3

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

Q1) \(x^2 + 10x+5 =0\) [ \(x=-5 ± \sqrt{20}\) ]

Q1) \(x^2 + 3x-8 =0\) [ \(x= \)-1\(\frac{1}{2}\) ± \( \sqrt{{ 10\frac{1}{4} }}\)]

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

Q2) \(x^2 + 8x-5 =0\) [ \(x=-4 ± \sqrt{21}\) ]

Q2) \(x^2 + 13x-2 =0\) [ \(x= \)-6\(\frac{1}{2}\) ± \( \sqrt{{ 44\frac{1}{4} }}\)]

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

Q3) \(x^2 + 10x-7 =0\) [ \(x=-5 ± \sqrt{32}\) ]

Q3) \(x^2 + 5x-6 =0\) [ \(x= \)-2\(\frac{1}{2}\) ± \( \sqrt{{ 12\frac{1}{4} }}\)]

Q4) \(x^2 + 6x =0 \) [ \( x= 0 \) or \( x= -6 \)
]

Q4) \(x^2 + 8x+6 =0\) [ \(x=-4 ± \sqrt{10}\) ]

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

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

Q5) \(x^2 + 8x+5 =0\) [ \(x=-4 ± \sqrt{11}\) ]

Q5) \(x^2 + 9x-8 =0\) [ \(x= \)-4\(\frac{1}{2}\) ± \( \sqrt{{ 28\frac{1}{4} }}\)]

Q6) \(x^2 -4x =0 \) [ \( x= 4 \) or \( x= 0 \)
]

Q6) \(x^2 + 14x-5 =0\) [ \(x=-7 ± \sqrt{54}\) ]

Q6) \(x^2 + 15x-8 =0\) [ \(x= \)-7\(\frac{1}{2}\) ± \( \sqrt{{ 64\frac{1}{4} }}\)]

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

Q7) \(x^2 + 10x+8 =0\) [ \(x=-5 ± \sqrt{17}\) ]

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

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

Q8) \(x^2 + 10x+4 =0\) [ \(x=-5 ± \sqrt{21}\) ]

Q8) \(x^2 + 19x-10 =0\) [ \(x= \)-9\(\frac{1}{2}\) ± \( \sqrt{{ 100\frac{1}{4} }}\)]

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

Q9) \(x^2 + 16x+2 =0\) [ \(x=-8 ± \sqrt{62}\) ]

Q9) \(x^2 + 15x-2 =0\) [ \(x= \)-7\(\frac{1}{2}\) ± \( \sqrt{{ 58\frac{1}{4} }}\)]

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

Q10) \(x^2 + 12x-6 =0\) [ \(x=-6 ± \sqrt{42}\) ]

Q10) \(x^2 + 5x-10 =0\) [ \(x= \)-2\(\frac{1}{2}\) ± \( \sqrt{{ 16\frac{1}{4} }}\)]