A monic quadratic equation has solutions x = \pm 5. What was the equation?
Solve the following equations:
x^{2} = 25
x^{2} - 25 = 0
\dfrac{x^{2}}{25} - 3 = 6
\left(x - 7\right)^{2} = 81
\left(7 - x\right)^{2} = 81
\left( 4 x + 3\right)^{2} = 64
\left(x - 4\right)^{2} = 10
How many real solutions does the equation x^{2} + 64 = 0 have?
Solve the following equations:
- 3 m \left(m + 2\right) = 0
\dfrac{m}{6} \left(m - 10\right) = 0
\left(x - 7\right) \left(x - 6\right) = 0
\left( 4 x - 17\right) \left( 3 x + 11\right) = 0
x^{2} + 19 x + 90 = 0
x^{2} + 6 x - 55 = 0
x^{2} - 17 x + 72 = 0
x^{2} - 5 x - 14 = 0
- x^{2} + x + 20 = 0
\dfrac{x^{2} - 5 x}{8} = 3
3 y - 15 y^{2} = 0
x^{2} - 64 = 0
m^{2} = m + 20
4 x^{2} + 8 x - 32 = 0
x^{2} - 20 x + 100 = 0
x \left(x + 2\right) = 48
Solve the following equations:
x - \dfrac{45}{x} = 4
\left(y + 1\right)^{2} = 4 y + 4
\left( 5 x^{2} + 13 x + 6\right) \left( 2 x^{2} + 13 x + 20\right) = 0
\dfrac{12 + 11 x}{5 x} = x
\dfrac{x + 1}{2} - \dfrac{x + 2}{3} = \dfrac{1 - x}{3 x + 1}
\dfrac{7}{x \left(x + 3\right)} + 5 = \dfrac{x + 4}{x}
Write down a monic quadratic equation that has two solutions, 7 and - 4. Write the equation in factorised form.
Form a monic quadratic equation which has solutions x = - 3 and x = - 5. Write the equation in expanded form.
Consider the equation x^{2} - 3 x = 6. What should be added to both sides of the equation in order to complete the square?
For each equation below, complete the square by completing each statement:
x^{2} + 4 x + ⬚ = \left(x + ⬚\right)^{2}
x^{2}-⬚x+16 = \left(x - ⬚\right)^{2}
x^{2}-\dfrac{7}{4}x+⬚= (x-⬚)^2
Solve the following by completing the square. Leave your answer in simplified surd form where necessary.
x^{2} - 6 x - 16 = 0
x^{2} + 5 x + 6 = 0
2 x^{2} - 20 x - 32 = 0
x^{2} + 18 x + 32 = 0
Solve the following equations by using the quadratic formula:
x^{2} + 11 x + 28 = 0
x^{2} - 5 x + 6 = 0
4 x^{2} + 6 x + 2 = 0
- 10 + 23 x + 5 x^{2} = 0
x^{2} - 5 x + \dfrac{9}{4} = 0
- 6 - 13 x + 5 x^{2} = 0
Solve the following equations, leaving your answer in surd form:
4 x^{2} - x - 10 = 0
- 2 x^{2} - 15 x - 4 = 0
\dfrac{3 x + 1}{3 x - 1} - \dfrac{3 x - 1}{3 x + 1} = 5
Solve 3 x \left(x + 4\right) = - 3 x + 4, giving your answers to 2 decimal places.
Use the quadratic formula to solve 5 x^{2} + 9 x + 2 = 0. Round your answers to the nearest thousandth.
Solve the following equations:
\left(3 - 3 x\right)^{2} = 0
x^{2} + 12 x = 0
4 y - 24 y^{2} = 0
y^{2} = 20 y
x^{2} = x + 12
m^{2} - 27 m = - 182
\dfrac{x^{2} - 4 x}{2} = 16
\left(y + 1\right)^{2} = 4 y + 4
- 4 x^{2} + 25 x - 36 = 0
4 x^{2} + 17 x + 15 = 0
Solve the following equations:
4 x^{2} - 7 x - 15 = 0
5 x^{2} + 14 x + 8 = 0
4 x^{2} - 17 x + 15 = 0
3 x^{2} - 7 x - 20 = 0
\dfrac{2 x^{2} - 19 x}{3} = 20