Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2+3x=-2x-13
-
Equation cos(x)=-(1/2)
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Equation sin(x/3)=-1/2
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Equation |x^2-1|-|x-3|=7
- Express {x} in terms of y where:
- -14*x-16*y=14
- 16*x-17*y=-9
- -14*x-3*y=-5
- -16*x-20*y=6
- Integral of d{x}:
- 96
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Identical expressions
- (3x- eight)^ two -(4x+ six)^ two +(5x- two)(5x+ two)= ninety-six
- (3x minus 8) squared minus (4x plus 6) squared plus (5x minus 2)(5x plus 2) equally 96
- (3x minus eight) to the power of two minus (4x plus six) to the power of two plus (5x minus two)(5x plus two) equally ninety minus six
- (3x-8)2-(4x+6)2+(5x-2)(5x+2)=96
- 3x-82-4x+62+5x-25x+2=96
- (3x-8)²-(4x+6)²+(5x-2)(5x+2)=96
- (3x-8) to the power of 2-(4x+6) to the power of 2+(5x-2)(5x+2)=96
- 3x-8^2-4x+6^2+5x-25x+2=96
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Similar expressions
- (3x-8)^2+(4x+6)^2+(5x-2)(5x+2)=96
- (3x-8)^2-(4x-6)^2+(5x-2)(5x+2)=96
- (3x-8)^2-(4x+6)^2+(5x-2)(5x-2)=96
- (3x+8)^2-(4x+6)^2+(5x-2)(5x+2)=96
- (3x-8)^2-(4x+6)^2+(5x+2)(5x+2)=96
- (3x-8)^2-(4x+6)^2-(5x-2)(5x+2)=96
(3x-8)^2-(4x+6)^2+(5x-2)(5x+2)=96 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
2 2 (3*x - 8) - (4*x + 6) + (5*x - 2)*(5*x + 2) = 96
$$\left(5 x - 2\right) \left(5 x + 2\right) + \left(\left(3 x - 8\right)^{2} - \left(4 x + 6\right)^{2}\right) = 96$$
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$\left(5 x - 2\right) \left(5 x + 2\right) + \left(\left(3 x - 8\right)^{2} - \left(4 x + 6\right)^{2}\right) = 96$$
to
$$\left(\left(5 x - 2\right) \left(5 x + 2\right) + \left(\left(3 x - 8\right)^{2} - \left(4 x + 6\right)^{2}\right)\right) - 96 = 0$$
Expand the expression in the equation
$$\left(\left(5 x - 2\right) \left(5 x + 2\right) + \left(\left(3 x - 8\right)^{2} - \left(4 x + 6\right)^{2}\right)\right) - 96 = 0$$
We get the quadratic equation
$$18 x^{2} - 96 x - 72 = 0$$
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
$$a = 18$$
$$b = -96$$
$$c = -72$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 6$$
$$x_{2} = - \frac{2}{3}$$
left part with negative sign.
The equation is transformed from
$$\left(5 x - 2\right) \left(5 x + 2\right) + \left(\left(3 x - 8\right)^{2} - \left(4 x + 6\right)^{2}\right) = 96$$
to
$$\left(\left(5 x - 2\right) \left(5 x + 2\right) + \left(\left(3 x - 8\right)^{2} - \left(4 x + 6\right)^{2}\right)\right) - 96 = 0$$
Expand the expression in the equation
$$\left(\left(5 x - 2\right) \left(5 x + 2\right) + \left(\left(3 x - 8\right)^{2} - \left(4 x + 6\right)^{2}\right)\right) - 96 = 0$$
We get the quadratic equation
$$18 x^{2} - 96 x - 72 = 0$$
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
$$a = 18$$
$$b = -96$$
$$c = -72$$
, then
D = b^2 - 4 * a * c =
(-96)^2 - 4 * (18) * (-72) = 14400
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 6$$
$$x_{2} = - \frac{2}{3}$$
Sum and product of roots
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sum
6 - 2/3
$$- \frac{2}{3} + 6$$
=
16/3
$$\frac{16}{3}$$
product
6*(-2) ------ 3
$$\frac{\left(-2\right) 6}{3}$$
=
-4
$$-4$$
-4