Question

4. Solve the following quadratics using the best method. 3/2 x^2 - 4 = 8 25x^2 -5x = 0 y = 4x² + 10x - 8

Answer 1

1.

`\begin{gathered} (3)/(2)x^2\text{ - 4 = 8} \\ \text{collect like terms} \\ (3)/(2)x^2\text{ = 12} \\ 3x^2\text{ = 2 x 12} \\ 3x^2\text{ = 24} \\ 3x^2\text{ - 24 = 0} \\ 3(x^2\text{ - 8) = 0} \\ x^2\text{ - 8 = 0} \\ x\text{ = }\pm\sqrt[]{8} \\ x\text{ = }\pm2\sqrt[]{2} \end{gathered}`

2.

`\begin{gathered} 25x^2\text{ - 5x = 0} \\ \text{First, factor 5x out first.} \\ 5x(5x\text{ - 1) = 0} \\ 5x\text{ = 0 or 5x - 1 = 0} \\ x\text{ = }(0)/(5)\text{ or 5x = 1} \\ x\text{ = 0 or x = }(1)/(5) \end{gathered}`

3.

`\begin{gathered} 4x^2\text{ + 10x - 8 = 0} \\ \text{Divide through by 2} \\ 2x^2\text{ + 5x - 4 = 0} \\ \text{use quadratic equation formula to find x.} \\ a\text{ = 2 b = 5 and c = -4} \\ x\text{ = }\frac{-b\text{ }\pm\text{ }\sqrt[]{b^2\text{ - 4ac}}}{2a} \\ =\text{ }\frac{-5\pm\sqrt[]{5^2\text{ - 4x2x(-5)}}}{2\text{ x 2}} \\ =\text{ }\frac{-5\pm\sqrt[]{25+40}}{4} \\ =\text{ }\frac{-5\pm\sqrt[]{65}}{4} \\ =\text{ }\frac{-5\text{ }\pm8.06}{4} \\ x\text{ = }\frac{-5\text{ - 8.60}}{4}\text{ or }\frac{-5\text{ + 8.06}}{4} \\ x=\text{ }-3.27\text{ or 0.765} \end{gathered}`