Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 9-8*x=-9*x+15
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Equation 4^x-1/2-6*2^x-1+3=0
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Equation x^2-25=0
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Equation x^2+6*x+7=0
- Express {x} in terms of y where:
- -16*x-9*y=-1
- -15*x+7*y=1
- 18*x-6*y=7
- -19*x+16*y=-9
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Identical expressions
- 7x^ two + eighteen *x+ five = zero
- 7x squared plus 18 multiply by x plus 5 equally 0
- 7x to the power of two plus eighteen multiply by x plus five equally zero
- 7x2+18*x+5=0
- 7x²+18*x+5=0
- 7x to the power of 2+18*x+5=0
- 7x^2+18x+5=0
- 7x2+18x+5=0
- 7x^2+18*x+5=O
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Similar expressions
- 7x^2+18*x-5=0
- 7x^2-18*x+5=0
7x^2+18*x+5=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
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
$$a = 7$$
$$b = 18$$
$$c = 5$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{9}{7} + \frac{\sqrt{46}}{7}$$
$$x_{2} = - \frac{9}{7} - \frac{\sqrt{46}}{7}$$
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
$$a = 7$$
$$b = 18$$
$$c = 5$$
, then
D = b^2 - 4 * a * c =
(18)^2 - 4 * (7) * (5) = 184
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{9}{7} + \frac{\sqrt{46}}{7}$$
$$x_{2} = - \frac{9}{7} - \frac{\sqrt{46}}{7}$$
Vieta's Theorem
rewrite the equation
$$\left(7 x^{2} + 18 x\right) + 5 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{18 x}{7} + \frac{5}{7} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{18}{7}$$
$$q = \frac{c}{a}$$
$$q = \frac{5}{7}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{18}{7}$$
$$x_{1} x_{2} = \frac{5}{7}$$
$$\left(7 x^{2} + 18 x\right) + 5 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{18 x}{7} + \frac{5}{7} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{18}{7}$$
$$q = \frac{c}{a}$$
$$q = \frac{5}{7}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{18}{7}$$
$$x_{1} x_{2} = \frac{5}{7}$$
Sum and product of roots
[src]
sum
____ ____ 9 \/ 46 9 \/ 46 - - - ------ + - - + ------ 7 7 7 7
$$\left(- \frac{9}{7} - \frac{\sqrt{46}}{7}\right) + \left(- \frac{9}{7} + \frac{\sqrt{46}}{7}\right)$$
=
-18/7
$$- \frac{18}{7}$$
product
/ ____\ / ____\ | 9 \/ 46 | | 9 \/ 46 | |- - - ------|*|- - + ------| \ 7 7 / \ 7 7 /
$$\left(- \frac{9}{7} - \frac{\sqrt{46}}{7}\right) \left(- \frac{9}{7} + \frac{\sqrt{46}}{7}\right)$$
=
5/7
$$\frac{5}{7}$$
5/7
Rapid solution
[src]
____
9 \/ 46
x1 = - - - ------
7 7
$$x_{1} = - \frac{9}{7} - \frac{\sqrt{46}}{7}$$
____
9 \/ 46
x2 = - - + ------
7 7
$$x_{2} = - \frac{9}{7} + \frac{\sqrt{46}}{7}$$
x2 = -9/7 + sqrt(46)/7