Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 15-x=8
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Equation 2x=5
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Equation 3/8*x+15=1/6*x+10
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Equation (x-4)^2-25=0
- Express {x} in terms of y where:
- -9*x+8*y=-11
- 2*x+10*y=-10
- 18*x-7*y=-13
- -11*x-3*y=-15
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Identical expressions
- (x- four)^ two - twenty-five = zero
- (x minus 4) squared minus 25 equally 0
- (x minus four) to the power of two minus twenty minus five equally zero
- (x-4)2-25=0
- x-42-25=0
- (x-4)²-25=0
- (x-4) to the power of 2-25=0
- x-4^2-25=0
- (x-4)^2-25=O
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Similar expressions
- (x-4)^2+25=0
- (x+4)^2-25=0
(x-4)^2-25=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x - 4\right)^{2} - 25 = 0$$
We get the quadratic equation
$$x^{2} - 8 x - 9 = 0$$
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
$$a = 1$$
$$b = -8$$
$$c = -9$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 9$$
$$x_{2} = -1$$
$$\left(x - 4\right)^{2} - 25 = 0$$
We get the quadratic equation
$$x^{2} - 8 x - 9 = 0$$
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
$$a = 1$$
$$b = -8$$
$$c = -9$$
, then
D = b^2 - 4 * a * c =
(-8)^2 - 4 * (1) * (-9) = 100
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 9$$
$$x_{2} = -1$$
The graph