Solve the quadratic equation x^2-10+34=0?

Method 1 : completing square

x² - 10x + 34 = 0
x² - 10x = -34
x² - 2(5)x + 5² = -34 + 5²
(x - 5)² = -9
x - 5 = √(-9) or x - 5 = -√(-9)
x - 5 = 3i or x - 5 = -3i ...... where i = √(-1)
x = 5 + 3i or x = 5 - 3i


Method 2 : using the formula x = [-b ± √(b² - 4ac)] / (2a)

x² - 10x + 34 = 0
x = {-(-10) ± √[(-10)² - 4(1)(34)]} / 2
x = [10 ± √(100 - 136)] / 2
x = [10 ± √(-36)]/2
x = [10 ± 6i]/2
x = 5 + 3i or x = 5 - 3i

This equation is of form ax^2+bx+c
a = 1 b = -10 c = 34
x=[-b+/-sqrt(b^2-4ac)]/2a]
x=[10 +/-sqrt(-10^2-4(1)(34)]/(2)(1)
discriminant is b^2-4ac =-36
i^2 = -1, so √i^2 = i
No real roots: The complex roots are
x=[10 +i √(36)] / (2)(1)
x=[10 -i √(36)] / (2)(1)
x=[10+i6] / 2
x= 5 + 3i -----(1)
x=[10-i6] / 2
x = 5-3i -------(2)

(1) & (2) are solutions

x^2+24=0
x^2=-24
There are no real solutions as you cant take the square root of a negative number.
If your doing imaginary numbers then it is √24i

if you meant x^2-10x+34=0, then completing the square, gives you x^2-10x+25=-9

you should be able to take it from there