Mister Exam
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Identical expressions
- 16x+ nine -4x²= nine
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- 16x plus nine minus 4x² equally nine
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Similar expressions
- 16x+9+4x²=9
- 16x-9-4x²=9
16x+9-4x²=9 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$- 4 x^{2} + \left(16 x + 9\right) = 9$$
to
$$\left(- 4 x^{2} + \left(16 x + 9\right)\right) - 9 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = -4$$
$$b = 16$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 0$$
$$x_{2} = 4$$
left part with negative sign.
The equation is transformed from
$$- 4 x^{2} + \left(16 x + 9\right) = 9$$
to
$$\left(- 4 x^{2} + \left(16 x + 9\right)\right) - 9 = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = -4$$
$$b = 16$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(16)^2 - 4 * (-4) * (0) = 256
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 0$$
$$x_{2} = 4$$
Vieta's Theorem
rewrite the equation
$$- 4 x^{2} + \left(16 x + 9\right) = 9$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 4 x = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = 0$$
$$- 4 x^{2} + \left(16 x + 9\right) = 9$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 4 x = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = 0$$