Mister Exam
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Identical expressions
- (5x- fifteen)^ two = zero
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- (5x-15)2=0
- 5x-152=0
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Similar expressions
- (5x+15)^2=0
(5x-15)^2=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(5 x - 15\right)^{2} = 0$$
We get the quadratic equation
$$25 x^{2} - 150 x + 225 = 0$$
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
$$a = 25$$
$$b = -150$$
$$c = 225$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = 3$$
$$\left(5 x - 15\right)^{2} = 0$$
We get the quadratic equation
$$25 x^{2} - 150 x + 225 = 0$$
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
$$a = 25$$
$$b = -150$$
$$c = 225$$
, then
D = b^2 - 4 * a * c =
(-150)^2 - 4 * (25) * (225) = 0
Because D = 0, then the equation has one root.
x = -b/2a = --150/2/(25)
$$x_{1} = 3$$