Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation x+y=15
- Equation a^2*x^2-21*a^2+a*x+1=0
-
Equation 5-x=4(x-3)
-
Equation -(-y+4)+2*y+1=0
- Express {x} in terms of y where:
- -16*x-20*y=-13
- 4*x+5*y=7
- -12*x-2*y=7
- -5*x+7*y=-18
- Graphing y =:
- (x+5)^2
- Integral of d{x}:
- (x+5)^2
- Derivative of:
-
(x+5)^2
-
Identical expressions
- (x+ five)^ two = five
- (x plus 5) squared equally 5
- (x plus five) to the power of two equally five
- (x+5)2=5
- x+52=5
- (x+5)²=5
- (x+5) to the power of 2=5
- x+5^2=5
-
Similar expressions
- (x-5)^2=5
(x+5)^2=5 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
$$\left(x + 5\right)^{2} = 5$$
to
$$\left(x + 5\right)^{2} - 5 = 0$$
Expand the expression in the equation
$$\left(x + 5\right)^{2} - 5 = 0$$
We get the quadratic equation
$$x^{2} + 10 x + 20 = 0$$
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
$$a = 1$$
$$b = 10$$
$$c = 20$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -5 + \sqrt{5}$$
$$x_{2} = -5 - \sqrt{5}$$
left part with negative sign.
The equation is transformed from
$$\left(x + 5\right)^{2} = 5$$
to
$$\left(x + 5\right)^{2} - 5 = 0$$
Expand the expression in the equation
$$\left(x + 5\right)^{2} - 5 = 0$$
We get the quadratic equation
$$x^{2} + 10 x + 20 = 0$$
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
$$a = 1$$
$$b = 10$$
$$c = 20$$
, then
D = b^2 - 4 * a * c =
(10)^2 - 4 * (1) * (20) = 20
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -5 + \sqrt{5}$$
$$x_{2} = -5 - \sqrt{5}$$
Sum and product of roots
[src]
sum
___ ___ -5 - \/ 5 + -5 + \/ 5
$$\left(-5 - \sqrt{5}\right) + \left(-5 + \sqrt{5}\right)$$
=
-10
$$-10$$
product
/ ___\ / ___\ \-5 - \/ 5 /*\-5 + \/ 5 /
$$\left(-5 - \sqrt{5}\right) \left(-5 + \sqrt{5}\right)$$
=
20
$$20$$
20
Rapid solution
[src]
___ x1 = -5 - \/ 5
$$x_{1} = -5 - \sqrt{5}$$
___ x2 = -5 + \/ 5
$$x_{2} = -5 + \sqrt{5}$$
x2 = -5 + sqrt(5)
The graph