Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation x-y=7
-
Equation 1/(x+6)=2
-
Equation (x-4)^2-x^2=0
-
Equation 6/(x+5)=-5
- Express {x} in terms of y where:
- 7*x-1*y=-7
- 10*x-15*y=16
- -14*x-12*y=5
- 13*x-12*y=19
-
Identical expressions
- (eight *y+ five)^ two - one hundred and twenty-eight = eighty *y- sixty-four ^ two + twenty-five
- (8 multiply by y plus 5) squared minus 128 equally 80 multiply by y minus 64 squared plus 25
- (eight multiply by y plus five) to the power of two minus one hundred and twenty minus eight equally eighty multiply by y minus sixty minus four to the power of two plus twenty minus five
- (8*y+5)2-128=80*y-642+25
- 8*y+52-128=80*y-642+25
- (8*y+5)²-128=80*y-64²+25
- (8*y+5) to the power of 2-128=80*y-64 to the power of 2+25
- (8y+5)^2-128=80y-64^2+25
- (8y+5)2-128=80y-642+25
- 8y+52-128=80y-642+25
- 8y+5^2-128=80y-64^2+25
-
Similar expressions
- (8*y-5)^2-128=80*y-64^2+25
- (8*y+5)^2-128=80*y+64^2+25
- (8*y+5)^2+128=80*y-64^2+25
- (8*y+5)^2-128=80*y-64^2-25
(8*y+5)^2-128=80*y-64^2+25 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 2 (8*y + 5) - 128 = 80*y - 64 + 25
$$\left(8 y + 5\right)^{2} - 128 = 80 y - 64^{2} + 25$$
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$\left(8 y + 5\right)^{2} - 128 = 80 y - 64^{2} + 25$$
to
$$\left(\left(8 y + 5\right)^{2} - 128\right) - \left(80 y - 4096 + 25\right) = 0$$
Expand the expression in the equation
$$\left(\left(8 y + 5\right)^{2} - 128\right) - \left(80 y - 4096 + 25\right) = 0$$
We get the quadratic equation
$$64 y^{2} + 3968 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 64$$
$$b = 0$$
$$c = 3968$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$y_{1} = \sqrt{62} i$$
Simplify
$$y_{2} = - \sqrt{62} i$$
Simplify
left part with negative sign.
The equation is transformed from
$$\left(8 y + 5\right)^{2} - 128 = 80 y - 64^{2} + 25$$
to
$$\left(\left(8 y + 5\right)^{2} - 128\right) - \left(80 y - 4096 + 25\right) = 0$$
Expand the expression in the equation
$$\left(\left(8 y + 5\right)^{2} - 128\right) - \left(80 y - 4096 + 25\right) = 0$$
We get the quadratic equation
$$64 y^{2} + 3968 = 0$$
This equation is of the form
a*y^2 + b*y + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 64$$
$$b = 0$$
$$c = 3968$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (64) * (3968) = -1015808
Because D<0, then the equation
has no real roots,
but complex roots is exists.
y1 = (-b + sqrt(D)) / (2*a)
y2 = (-b - sqrt(D)) / (2*a)
or
$$y_{1} = \sqrt{62} i$$
Simplify
$$y_{2} = - \sqrt{62} i$$
Simplify
Sum and product of roots
[src]
sum
____ ____ 0 - I*\/ 62 + I*\/ 62
$$\left(0 - \sqrt{62} i\right) + \sqrt{62} i$$
=
0
$$0$$
product
____ ____ 1*-I*\/ 62 *I*\/ 62
$$\sqrt{62} i 1 \left(- \sqrt{62} i\right)$$
=
62
$$62$$
62
Rapid solution
[src]
____ y1 = -I*\/ 62
$$y_{1} = - \sqrt{62} i$$
____ y2 = I*\/ 62
$$y_{2} = \sqrt{62} i$$
The graph