Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x+5=12
-
Equation -4x+9=-19
-
Equation x^2+20*x+100=0
-
Equation 2x+1-20x+15=6x+4
- Express {x} in terms of y where:
- -19*x+3*y=-13
- -11*x-12*y=16
- 17*x+13*y=3
- -4*x+10*y=-6
-
Identical expressions
- (8x+x)(x^ two -8x+ sixty-four)=x(x- two)^ two +4x^ two
- (8x plus x)(x squared minus 8x plus 64) equally x(x minus 2) squared plus 4x squared
- (8x plus x)(x to the power of two minus 8x plus sixty minus four) equally x(x minus two) to the power of two plus 4x to the power of two
- (8x+x)(x2-8x+64)=x(x-2)2+4x2
- 8x+xx2-8x+64=xx-22+4x2
- (8x+x)(x²-8x+64)=x(x-2)²+4x²
- (8x+x)(x to the power of 2-8x+64)=x(x-2) to the power of 2+4x to the power of 2
- 8x+xx^2-8x+64=xx-2^2+4x^2
-
Similar expressions
- (8x-x)(x^2-8x+64)=x(x-2)^2+4x^2
- (8x+x)(x^2+8x+64)=x(x-2)^2+4x^2
- (8x+x)(x^2-8x+64)=x(x-2)^2-4x^2
- (8x+x)(x^2-8x+64)=x(x+2)^2+4x^2
- (8x+x)(x^2-8x-64)=x(x-2)^2+4x^2
(8x+x)(x^2-8x+64)=x(x-2)^2+4x^2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/ 2 \ 2 2 (8*x + x)*\x - 8*x + 64/ = x*(x - 2) + 4*x
$$\left(x + 8 x\right) \left(\left(x^{2} - 8 x\right) + 64\right) = 4 x^{2} + x \left(x - 2\right)^{2}$$
Detail solution
Given the equation:
$$\left(x + 8 x\right) \left(\left(x^{2} - 8 x\right) + 64\right) = 4 x^{2} + x \left(x - 2\right)^{2}$$
transform:
Take common factor from the equation
$$4 x \left(2 x^{2} - 18 x + 143\right) = 0$$
Because the right side of the equation is zero, then the solution of the equation is exists if at least one of the multipliers in the left side of the equation equal to zero.
We get the equations
$$4 x = 0$$
$$2 x^{2} - 18 x + 143 = 0$$
solve the resulting equation:
1.
$$4 x = 0$$
Divide both parts of the equation by 4
We get the answer: x1 = 0
2.
$$2 x^{2} - 18 x + 143 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{2} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{3} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 2$$
$$b = -18$$
$$c = 143$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{2} = \frac{9}{2} + \frac{\sqrt{205} i}{2}$$
$$x_{3} = \frac{9}{2} - \frac{\sqrt{205} i}{2}$$
The final answer:
$$x_{1} = 0$$
$$x_{2} = \frac{9}{2} + \frac{\sqrt{205} i}{2}$$
$$x_{3} = \frac{9}{2} - \frac{\sqrt{205} i}{2}$$
$$\left(x + 8 x\right) \left(\left(x^{2} - 8 x\right) + 64\right) = 4 x^{2} + x \left(x - 2\right)^{2}$$
transform:
Take common factor from the equation
$$4 x \left(2 x^{2} - 18 x + 143\right) = 0$$
Because the right side of the equation is zero, then the solution of the equation is exists if at least one of the multipliers in the left side of the equation equal to zero.
We get the equations
$$4 x = 0$$
$$2 x^{2} - 18 x + 143 = 0$$
solve the resulting equation:
1.
$$4 x = 0$$
Divide both parts of the equation by 4
x = 0 / (4)
We get the answer: x1 = 0
2.
$$2 x^{2} - 18 x + 143 = 0$$
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:
$$x_{2} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{3} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 2$$
$$b = -18$$
$$c = 143$$
, then
D = b^2 - 4 * a * c =
(-18)^2 - 4 * (2) * (143) = -820
Because D<0, then the equation
has no real roots,
but complex roots is exists.
x2 = (-b + sqrt(D)) / (2*a)
x3 = (-b - sqrt(D)) / (2*a)
or
$$x_{2} = \frac{9}{2} + \frac{\sqrt{205} i}{2}$$
$$x_{3} = \frac{9}{2} - \frac{\sqrt{205} i}{2}$$
The final answer:
$$x_{1} = 0$$
$$x_{2} = \frac{9}{2} + \frac{\sqrt{205} i}{2}$$
$$x_{3} = \frac{9}{2} - \frac{\sqrt{205} i}{2}$$
Sum and product of roots
[src]
sum
_____ _____ 9 I*\/ 205 9 I*\/ 205 - - --------- + - + --------- 2 2 2 2
$$\left(\frac{9}{2} - \frac{\sqrt{205} i}{2}\right) + \left(\frac{9}{2} + \frac{\sqrt{205} i}{2}\right)$$
=
9
$$9$$
product
/ _____\ / _____\ |9 I*\/ 205 | |9 I*\/ 205 | 0*|- - ---------|*|- + ---------| \2 2 / \2 2 /
$$0 \left(\frac{9}{2} - \frac{\sqrt{205} i}{2}\right) \left(\frac{9}{2} + \frac{\sqrt{205} i}{2}\right)$$
=
0
$$0$$
0
Rapid solution
[src]
x1 = 0
$$x_{1} = 0$$
_____
9 I*\/ 205
x2 = - - ---------
2 2
$$x_{2} = \frac{9}{2} - \frac{\sqrt{205} i}{2}$$
_____
9 I*\/ 205
x3 = - + ---------
2 2
$$x_{3} = \frac{9}{2} + \frac{\sqrt{205} i}{2}$$
x3 = 9/2 + sqrt(205)*i/2
Numerical answer
[src]
x1 = 4.5 + 7.15891053163818*i
x2 = 4.5 - 7.15891053163818*i
x3 = 0.0
x3 = 0.0