Question

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

Answer 1

`x=(5\pm√(10))/(2)`

Explanation:

`4x^2-20x+25=10\\(2x)^2-2\cdot2x\cdot5+5^2=10\\(2x-5)^2=10\\2x-5=\pm√(10) \\2x=5\pm√(10) \\x=(5\pm√(10))/(2) \\\\x_1=(5-√(10))/(2); \ x_2=(5+√(10))/(2)`

Answer 2

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{ = }(-b\pm√(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{ }√(160)}{8} \\ \\ x\text{ = }\frac{20\text{ }\pm\text{ 4}√(10)}{8} \\ \\ x\text{ = }\frac{5\text{ + }√(10)}{2}\text{ or x = }\frac{5\text{ - }√(10)}{2} \\ \end{gathered}`

Final Answer -

x = (5 + √10)/2 and

x = (5 - √10)/2