-4x2 + 5x + 6 = 0
Multiply through by -1: 4x2 - 5x - 6 = 0 (I prefer the leading coefficient to be >0)
4x2 - 8x + 3x - 6 = 0
4x(x - 2) + 3(x - 2) = 0
(x - 2)(4x + 3) = 0
So x - 2 = 0 or 4x + 3 = 0
ie x = 2 or x = -3/4
4x2+50x = 0 4x(x+12.5) = 0 x = 0 or x = -12.5
The discriminant for the quadratic is b2-4ac = 302 - 4*4*45 = 900 - 720 = 180 Since 180 is not a perfect square, the roots of the equation are irrational and it is far from straightforward to solve such an equation by factoring.
If you can't factor it easily, use the quadratic formula.
4x2 plus 3=11
4x2 - 13 x + 3 = 0 (4x - 1)(x - 3) = 0 x = 3, 1/4
4x2 = -12x, divide both sides by 4x: x = -3
4x2+50x = 0 4x(x+12.5) = 0 x = 0 or x = -12.5
The discriminant for the quadratic is b2-4ac = 302 - 4*4*45 = 900 - 720 = 180 Since 180 is not a perfect square, the roots of the equation are irrational and it is far from straightforward to solve such an equation by factoring.
4x2 plus 3=11
If you can't factor it easily, use the quadratic formula.
First you need to solve for y. So write 4x2+y=16 so y=16-4x2 Now write f(x)=16-4x2
y=4x2+3x+8
4x2 - 13 x + 3 = 0 (4x - 1)(x - 3) = 0 x = 3, 1/4
x3 + 4x2 + 6x + 24 = (x2 + 6)(x + 4)
4x2+49x+90 = (4x+9)(x+10) when factored
There are four solutions to 9x4 plus 27x3 - 4x2 - 12x equals 0. One of the solutions is x = -3.
(4x - 32)(x - 2) so x = 2 or 8