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

Q1) \(x^2 + 5x-3 =0\) [ \(x= \)-2\(\frac{1}{2}\) ± \( \sqrt{{ 9\frac{1}{4} }}\)]

Q2) \(x^2 -8x =0 \) [ \( x= 8 \) or \( x= 0 \)
]

Q2) \(x^2 + 12x-3 =0\) [ \(x=-6 ± \sqrt{39}\) ]

Q2) \(x^2 + 11x-9 =0\) [ \(x= \)-5\(\frac{1}{2}\) ± \( \sqrt{{ 39\frac{1}{4} }}\)]

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

Q3) \(x^2 + 14x+9 =0\) [ \(x=-7 ± \sqrt{40}\) ]

Q3) \(x^2 + 7x-7 =0\) [ \(x= \)-3\(\frac{1}{2}\) ± \( \sqrt{{ 19\frac{1}{4} }}\)]

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

Q4) \(x^2 + 14x-4 =0\) [ \(x=-7 ± \sqrt{53}\) ]

Q4) \(x^2 + 15x-2 =0\) [ \(x= \)-7\(\frac{1}{2}\) ± \( \sqrt{{ 58\frac{1}{4} }}\)]

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

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

Q5) \(x^2 + 11x-2 =0\) [ \(x= \)-5\(\frac{1}{2}\) ± \( \sqrt{{ 32\frac{1}{4} }}\)]

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

Q6) \(x^2 + 14x+7 =0\) [ \(x=-7 ± \sqrt{42}\) ]

Q6) \(x^2 + 17x-4 =0\) [ \(x= \)-8\(\frac{1}{2}\) ± \( \sqrt{{ 76\frac{1}{4} }}\)]

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

Q7) \(x^2 + 14x+2 =0\) [ \(x=-7 ± \sqrt{47}\) ]

Q7) \(x^2 + 17x-8 =0\) [ \(x= \)-8\(\frac{1}{2}\) ± \( \sqrt{{ 80\frac{1}{4} }}\)]

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

Q8) \(x^2 + 8x+9 =0\) [ \(x=-4 ± \sqrt{7}\) ]

Q8) \(x^2 + 11x-5 =0\) [ \(x= \)-5\(\frac{1}{2}\) ± \( \sqrt{{ 35\frac{1}{4} }}\)]

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

Q9) \(x^2 + 12x-3 =0\) [ \(x=-6 ± \sqrt{39}\) ]

Q9) \(x^2 + 3x-7 =0\) [ \(x= \)-1\(\frac{1}{2}\) ± \( \sqrt{{ 9\frac{1}{4} }}\)]

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

Q10) \(x^2 + 16x+10 =0\) [ \(x=-8 ± \sqrt{54}\) ]

Q10) \(x^2 + 11x-10 =0\) [ \(x= \)-5\(\frac{1}{2}\) ± \( \sqrt{{ 40\frac{1}{4} }}\)]