Answer:
The equation has two solutions for x:
<u>x₁ = (8 + 10i)/2</u>
<u>x₂ = (8 - 10i)/2</u>
Step-by-step explanation:
Let's use the quadratic formula for solving for x in the equation:
X^2 - 8X + 41= 0
x² - 8x + 41 = 0
Let's recall that the quadratic formula is:
x = -b +/- (√b² - 4ac)/2a
Replacing with the real values, we have:
x = 8 +/- (√-8² - 4 * 1 * 41)/2 * 1
x = 8 +/- (√64 - 164)/2
x = 8 +/- (√-100)/2
x = 8 +/- (√-1 *100)/2
Let's recall that √-1 = i
x = 8 +/- 10i/2
<u>x₁ = (8 + 10i)/2</u>
<u>x₂ = (8 - 10i)/2</u>
X^2 - 10x + 8 =0
x^2 - 10 + (-10/2)^2 - (-10/2)^2 + 8 = 0
(x - 5)^2 - 25 + 8 = 0
(x - 5)^2 - 17 = 0
To be honest , this is the final step for this equation. It seems like there is no any suitable answer for this question..
To me , I think the best answer will be the third option.
x - 5 =0
x = 5
2x-10 = 0
2x = 10
x = 5
I guess this answer seems like legit.. So I will choose the third option.
The answer for this problem would be x equal to 430 cm and y is equal to 325. This is computed by establishing the equations. This first equation based on first statement would be x = 15 + y and the second would be 5x = 3y + 525. Then it is solve as follows:
5x = 3y + 525