Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2+11*x+30=0
-
Equation (-2-4t-1)²+(0+2t-1)²+(2+5t)²=9
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Equation 1/3*x=12
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Equation (|3*x-9|)-(|x+2|)=7
- Express {x} in terms of y where:
- 20*x-11*y=-8
- -12*x-20*y=7
- -9*x+7*y=14
- -8*x-4*y=-3
- Canonical form:
- (x+1)^2
- Integral of d{x}:
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(x+1)^2
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(2x-1)^2
- Derivative of:
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(x+1)^2
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(2x-1)^2
- Graphing y =:
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(2x-1)^2
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Identical expressions
- (x+ one)^ two =(two x- one)^2
- (x plus 1) squared equally (2x minus 1) squared
- (x plus one) to the power of two equally (two x minus one) squared
- (x+1)2=(2x-1)2
- x+12=2x-12
- (x+1)²=(2x-1)²
- (x+1) to the power of 2=(2x-1) to the power of 2
- x+1^2=2x-1^2
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Similar expressions
- (x+1)^2=(2x+1)^2
- (x-1)^2=(2x-1)^2
(x+1)^2=(2x-1)^2 equation
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The solution
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2 2 (x + 1) = (2*x - 1)
$$\left(x + 1\right)^{2} = \left(2 x - 1\right)^{2}$$
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$\left(x + 1\right)^{2} = \left(2 x - 1\right)^{2}$$
to
$$\left(x + 1\right)^{2} - \left(2 x - 1\right)^{2} = 0$$
Expand the expression in the equation
$$\left(x + 1\right)^{2} - \left(2 x - 1\right)^{2} = 0$$
We get the quadratic equation
$$- 3 x^{2} + 6 x = 0$$
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
$$a = -3$$
$$b = 6$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 0$$
$$x_{2} = 2$$
left part with negative sign.
The equation is transformed from
$$\left(x + 1\right)^{2} = \left(2 x - 1\right)^{2}$$
to
$$\left(x + 1\right)^{2} - \left(2 x - 1\right)^{2} = 0$$
Expand the expression in the equation
$$\left(x + 1\right)^{2} - \left(2 x - 1\right)^{2} = 0$$
We get the quadratic equation
$$- 3 x^{2} + 6 x = 0$$
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
$$a = -3$$
$$b = 6$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(6)^2 - 4 * (-3) * (0) = 36
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 0$$
$$x_{2} = 2$$
The graph