Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x-11)/(x-6)=11/16
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Equation 5*x=12
- Equation x^2+p*x+q=0
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Equation 2*sin(x)*cos(x)=0
- Express {x} in terms of y where:
- -4*x-12*y=10
- -20*x-7*y=-17
- -16*x-9*y=-5
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Identical expressions
- (9x- two)^ two -(x- seventeen)^ two = zero
- (9x minus 2) squared minus (x minus 17) squared equally 0
- (9x minus two) to the power of two minus (x minus seventeen) to the power of two equally zero
- (9x-2)2-(x-17)2=0
- 9x-22-x-172=0
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- 9x-2^2-x-17^2=0
- (9x-2)^2-(x-17)^2=O
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Similar expressions
- (9x-2)^2+(x-17)^2=0
- (9x+2)^2-(x-17)^2=0
- (9x-2)^2-(x+17)^2=0
(9x-2)^2-(x-17)^2=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
2 2 (9*x - 2) - (x - 17) = 0
$$- \left(x - 17\right)^{2} + \left(9 x - 2\right)^{2} = 0$$
Detail solution
Expand the expression in the equation
$$- \left(x - 17\right)^{2} + \left(9 x - 2\right)^{2} = 0$$
We get the quadratic equation
$$80 x^{2} - 2 x - 285 = 0$$
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
$$a = 80$$
$$b = -2$$
$$c = -285$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{19}{10}$$
$$x_{2} = - \frac{15}{8}$$
$$- \left(x - 17\right)^{2} + \left(9 x - 2\right)^{2} = 0$$
We get the quadratic equation
$$80 x^{2} - 2 x - 285 = 0$$
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
$$a = 80$$
$$b = -2$$
$$c = -285$$
, then
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (80) * (-285) = 91204
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{19}{10}$$
$$x_{2} = - \frac{15}{8}$$
Rapid solution
[src]
x1 = -15/8
$$x_{1} = - \frac{15}{8}$$
19
x2 = --
10
$$x_{2} = \frac{19}{10}$$
x2 = 19/10
Sum and product of roots
[src]
sum
19
-15/8 + --
10
$$- \frac{15}{8} + \frac{19}{10}$$
=
1/40
$$\frac{1}{40}$$
product
-15*19 ------ 8*10
$$- \frac{57}{16}$$
=
-57 ---- 16
$$- \frac{57}{16}$$
-57/16