Question

Which of the following are solutions to the equation below?Check all that apply.4x² -20x+ 25 = 10

Answer 1

Given -

4x² - 20x + 25 = 10

To Find -

Solutions to the equation =?

Step-by-Step Explanation -

We have to rearrange the equation first

4x² - 20x + 25 = 10

4x² - 20x + 25 - 10 = 0

4x² - 20x + 15 = 0

Here a = 4, b = -20, c = 15

Now, we put it in equation:

$x\text{ = }\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$\begin{gathered} x\text{ = }\frac{20\pm\sqrt{(-20)^2\text{ - 4\lparen4\rparen\lparen15\rparen}}}{2(4)} \\ \\ x\text{ = }\frac{20\text{ }\pm\text{ }\sqrt{400\text{ - 240}}}{8} \\ \\ x\text{ = }\frac{20\text{ }\pm\text{ }\sqrt{160}}{8} \\ \\ x\text{ = }\frac{20\text{ }\pm\text{ 4}\sqrt{10}}{8} \\ \\ x\text{ = }\frac{5\text{ + }\sqrt{10}}{2}\text{ or x = }\frac{5\text{ - }\sqrt{10}}{2} \\ \end{gathered}$

Final Answer -

x = (5 + √10)/2 and

x = (5 - √10)/2