Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2=5
-
Equation k^2+k=0
-
Equation 5x=0
-
Equation x^2-15=2x
- Express {x} in terms of y where:
- -4*x+3*y=9
- -2*x-19*y=-11
- -5*x+15*y=-15
- -1*x+7*y=-11
- Graphing y =:
- x^2-15
- 2x
- Factor polynomial:
- x^2-15
- Integral of d{x}:
- x^2-15
-
2x
- Derivative of:
-
2x
-
Identical expressions
- x^ two - fifteen =2x
- x squared minus 15 equally 2x
- x to the power of two minus fifteen equally 2x
- x2-15=2x
- x²-15=2x
- x to the power of 2-15=2x
-
Similar expressions
- (x+3)^4+2(x+3)^2-8=0
- x^2+15=2x
- 2^x=-4
x^2-15=2x 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
$$x^{2} - 15 = 2 x$$
to
$$- 2 x + \left(x^{2} - 15\right) = 0$$
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
$$a = 1$$
$$b = -2$$
$$c = -15$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 5$$
$$x_{2} = -3$$
left part with negative sign.
The equation is transformed from
$$x^{2} - 15 = 2 x$$
to
$$- 2 x + \left(x^{2} - 15\right) = 0$$
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
$$a = 1$$
$$b = -2$$
$$c = -15$$
, then
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (1) * (-15) = 64
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 5$$
$$x_{2} = -3$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -15$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -15$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -15$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -15$$
Sum and product of roots
[src]
sum
-3 + 5
$$-3 + 5$$
=
2
$$2$$
product
-3*5
$$- 15$$
=
-15
$$-15$$
-15
The graph