Question

question 7 of 10 which of the following are solutions to the equation below? check all that apply. 4x² - 20x + 25 = 10 a. x = (√10 + 5)/2 b. x = √10/2 + 5 c. x = -√10/2 + 5 d. x = (-√10 + 5)/2 e. x = -√15/2 f. x = √15/2

Explanation:

Step1: Rewrite the quadratic equation

First, rewrite $4x^{2}-20x + 25=10$ in standard form $ax^{2}+bx + c = 0$. Since $4x^{2}-20x+25 - 10=0$, we have $4x^{2}-20x + 15=0$. Here, $a = 4$, $b=-20$, $c = 15$.

Step2: Use the quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute $a = 4$, $b=-20$, $c = 15$ into it. First, calculate the discriminant $\Delta=b^{2}-4ac=(-20)^{2}-4\times4\times15=400 - 240 = 160$. Then $x=\frac{20\pm\sqrt{160}}{8}=\frac{20\pm4\sqrt{10}}{8}=\frac{5\pm\sqrt{10}}{2}$.

Answer:

A. $x=\frac{\sqrt{10}+5}{2}$
D. $x=\frac{-\sqrt{10}+5}{2}$