Question

Kindly explain why the equation below doesn't have solution
x^2-2x=-10

Answer 1

Moving the -10 over to the right
x^2-2x+10=0
Try solving this by factoring and you can't.
If you cant solve a quadratic by factoring, go for the quadratic equation.
Hopefully you have seen x = -b +or- the square root of b squared minus 4ac over 2 a.
The stuff under the square root in the quadratic eqn, b squared minus 4ac has to be positive since you can't take the square root of a negative number. For your example,
b squared - 4ac = (-2) squared - 4(1)10= a negative number.
Thus there is no solution.

Answer 2

x^2 - 2x = -10

x^2 - 2x + 10 = 0

If you use the quadratic formula, with a = 1, b = -2, and c = 10, the discriminant is:

b^2 - 4ac = (-2)^2 - 4(1)(10) = 4 - 40 = -36

When the discriminant is negative, there are no real roots.

Answer 3

ah okay :) negative numbers=no solution, no real roots :)

Answer 4

wow lets try this
\[x^2-2x=-10\]
\[(x-1)^2=-10+1=-9\] hmm a square cannot be negative
that is the real reason there is no real solution

Answer 5

A negative discriminant means no real roots because the discriminant is the expression inside the square root of the quadratic formula. So if the discriminant is negative that would mean taking the square root of a negative number which cannot be done with real numbers.

Answer 6

all that work is just to show you have a square on the left and a negative number on the right

Answer 7

Thank you :) ok, ill remember that :)