Solve the equation by completing the square.
-$$x ^ { 2 } + 70 = 17 x$$
A) $\{ 1,70 \}$
B) $\{ 10,7 \}$
C) $\{ - 70 , - 1 \}$
D) $\{ - 10 , - 7 \}$

Question

Quizplus · Accepted Answer

First, we move all the terms to one side to get 
$$x^2 - 17x + 70 = 0$$
To complete the square, we need to take half of the coefficient of the x term and square it. Half of -17 is -8.5, and $(-8.5)^2 = 72.25$. We add and subtract 72.25 inside the parentheses to get 
$$x^2 - 17x + 70 - 72.25 + 72.25 = 0$$
which simplifies to 
$$(x - 8.5)^2 = 2.25$$
Taking the square root of both sides, we get 
$$x - 8.5 = \pm1.5$$
Solving for x, we have 
$$x = 10 \text{  or  } x = 7$$
Therefore, the answer is B) $\{ 10,7 \}$.

Solve the Equation by Completing the Square x2+70=17xx ^ { 2 } + 70 = 17 xx2+70=17x

Solve the Equation by Completing the Square $x ^ { 2 } + 70 = 17 x$