4.01 Quadratic equations
The equation x^{2} - 144 = 0 has a positive integer solution of x = 12. Find its other solution.
Solve the following equations:
x^{2} = 2
x^{2} = 25
x^{2} = 121
x^{2} = 294
x^{2} - 121 = 0
x^{2} - 10 = 15
\dfrac{x^{2}}{16} - 2 = 2
\dfrac{x^{2}}{25} - 3 = 6
\left(x + 3\right)^{2} = 49
\left(x - 3\right)^{2} = 64
\left(x - 6\right)^{2} = 2
\left(2 - x\right)^{2} = 81
\left(x - 7\right)^{2} = 81
\left(7 - x\right)^{2} = 81
\left( 8 x + 9\right)^{2} = 256
81 x^{2} - 16 = 0
Solve the following equations:
x \left(x + 7\right) = 0
x \left( 2 x - 9\right) = 0
\left( 10 x - 9\right)^{2} = 0
\left( - 3 + 7 x\right)^{2} = 0
\left(x - 4\right) \left(x - 2\right) = 0
\left(x - 6\right) \left(x + 7\right) = 0
\left( 8 x - 5\right) \left( 3 x - 7\right) = 0
\left( 3 x + 8\right) \left( 5 x - 7\right) = 0
\left( 3 x - 17\right) \left( 2 x - d\right) = 0
Solve the following equations:
4 y^{2} = 100
25 y^{2} = 36
- 3 k^{2} = - 12
81 k^{2} + 8 = 24
- 25 v^{2} + 64 = 0
10 \left(p^{2} - 7\right) = 930
4 m \left(m + 5\right) = 0
\dfrac{m}{2} \left(m + 5\right) = 0
Solve the following equation for x, in terms of a and c. Assume a and c are positive.
a x^{2} - c = 0
The equation 4 x^{2} + k x + 16 = 0 has one solution: x = 2. Find the value of the coefficient k.
The equation a x^{2} - 32 x - 80=0 has one soulution: x = 4. Find the value of the coefficient of a.
The Widget and Trinket Emporium has released the forecast of its revenue over then next year. The revenue R (in dollars) at any point in time t (in months) is described by the equation:R = - \left(t - 12\right)^{2} + 4
When will the revenue be zero?
Neville needs a sheet of paper x \,\text{cm} by 13 \, \text{cm} for an origami giraffe. The local origami supply store only sells square sheets of paper.
The lower portion of the image below shows the excess area A of paper that will remain after Neville cuts out the x \,\text{cm} by 13 \,\text{cm} piece. The excess area, in square centimeter, is given by the equation:A = x \left(x - 13\right)
At what lengths x will the excess area be zero?
For what value of x will Neville be able to make an origami giraffe with the least amount of excess paper?
