To solve the given equations:
1) x + 6 = x^2
Rearrange the equation to set it equal to zero:x^2 - x - 6 = 0
Now, factor the quadratic equation:(x - 3)(x + 2) = 0
So, x = 3 or x = -2.
2) x^2 + 4 = 5x
Rearrange the equation to set it equal to zero:x^2 - 5x + 4 = 0
Now, factor the quadratic equation:(x - 4)(x - 1) = 0
So, x = 4 or x = 1.
3) (x - 3)(x + 3) = -5x - 13
Expand the left side of the equation:x^2 - 9 = -5x - 13
Rearrange the equation:x^2 + 5x - 4 = 0
Now, factor the quadratic equation:(x + 4)(x - 1) = 0
So, x = -4 or x = 1.
To solve the given equations:
1) x + 6 = x^2
Rearrange the equation to set it equal to zero:
x^2 - x - 6 = 0
Now, factor the quadratic equation:
(x - 3)(x + 2) = 0
So, x = 3 or x = -2.
2) x^2 + 4 = 5x
Rearrange the equation to set it equal to zero:
x^2 - 5x + 4 = 0
Now, factor the quadratic equation:
(x - 4)(x - 1) = 0
So, x = 4 or x = 1.
3) (x - 3)(x + 3) = -5x - 13
Expand the left side of the equation:
x^2 - 9 = -5x - 13
Rearrange the equation:
x^2 + 5x - 4 = 0
Now, factor the quadratic equation:
(x + 4)(x - 1) = 0
So, x = -4 or x = 1.