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- Equation:
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Equation sinx=1
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Equation x^2+5*x-14=0
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Equation x+4|x|=3
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Equation x^2+2*x=0
- Express {x} in terms of y where:
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Identical expressions
- (7x- two)^ two -(4x+ three)^ two = zero
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- 7x-2^2-4x+3^2=0
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Similar expressions
- (7x-2)^2-(4x-3)^2=0
- (7x+2)^2-(4x+3)^2=0
- (7x-2)^2+(4x+3)^2=0
(7x-2)^2-(4x+3)^2=0 equation
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The solution
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[src]
2 2 (7*x - 2) - (4*x + 3) = 0
$$- \left(4 x + 3\right)^{2} + \left(7 x - 2\right)^{2} = 0$$
Detail solution
Expand the expression in the equation
$$- \left(4 x + 3\right)^{2} + \left(7 x - 2\right)^{2} = 0$$
We get the quadratic equation
$$33 x^{2} - 52 x - 5 = 0$$
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
$$a = 33$$
$$b = -52$$
$$c = -5$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{5}{3}$$
$$x_{2} = - \frac{1}{11}$$
$$- \left(4 x + 3\right)^{2} + \left(7 x - 2\right)^{2} = 0$$
We get the quadratic equation
$$33 x^{2} - 52 x - 5 = 0$$
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
$$a = 33$$
$$b = -52$$
$$c = -5$$
, then
D = b^2 - 4 * a * c =
(-52)^2 - 4 * (33) * (-5) = 3364
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{5}{3}$$
$$x_{2} = - \frac{1}{11}$$
Rapid solution
[src]
x1 = -1/11
$$x_{1} = - \frac{1}{11}$$
x2 = 5/3
$$x_{2} = \frac{5}{3}$$
x2 = 5/3
Sum and product of roots
[src]
sum
-1/11 + 5/3
$$- \frac{1}{11} + \frac{5}{3}$$
=
52 -- 33
$$\frac{52}{33}$$
product
-5 ---- 11*3
$$- \frac{5}{33}$$
=
-5/33
$$- \frac{5}{33}$$
-5/33