4 X 2 X 30
$\exponential{ten}{2} - four x - 30 = 0 $
10=\sqrt{34}+2\approx vii.830951895
x=2-\sqrt{34}\approx -3.830951895
Share
x^{2}-4x-thirty=0
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and i when it is subtraction.
ten=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-thirty\right)}}{two}
This equation is in standard course: ax^{two}+bx+c=0. Substitute 1 for a, -four for b, and -xxx for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
ten=\frac{-\left(-4\correct)±\sqrt{16-4\left(-xxx\right)}}{ii}
Square -4.
x=\frac{-\left(-four\right)±\sqrt{16+120}}{2}
Multiply -4 times -xxx.
x=\frac{-\left(-4\right)±\sqrt{136}}{two}
Add together 16 to 120.
x=\frac{-\left(-4\right)±2\sqrt{34}}{2}
Take the square root of 136.
x=\frac{4±2\sqrt{34}}{2}
The opposite of -four is 4.
x=\frac{2\sqrt{34}+4}{2}
Now solve the equation x=\frac{4±2\sqrt{34}}{2} when ± is plus. Add 4 to 2\sqrt{34}.
10=\sqrt{34}+ii
Carve up 4+2\sqrt{34} by ii.
x=\frac{iv-2\sqrt{34}}{2}
At present solve the equation x=\frac{4±2\sqrt{34}}{2} when ± is minus. Subtract 2\sqrt{34} from 4.
10=2-\sqrt{34}
Split iv-2\sqrt{34} by two.
ten=\sqrt{34}+ii 10=ii-\sqrt{34}
The equation is now solved.
x^{two}-4x-30=0
Quadratic equations such every bit this one tin be solved by completing the square. In club to complete the square, the equation must first exist in the course ten^{2}+bx=c.
x^{2}-4x-xxx-\left(-30\right)=-\left(-thirty\correct)
Add thirty to both sides of the equation.
ten^{2}-4x=-\left(-xxx\right)
Subtracting -30 from itself leaves 0.
10^{two}-4x=30
Subtract -30 from 0.
ten^{2}-4x+\left(-2\right)^{2}=30+\left(-ii\correct)^{two}
Divide -4, the coefficient of the ten term, past 2 to get -2. Then add the foursquare of -ii to both sides of the equation. This step makes the left hand side of the equation a perfect foursquare.
x^{ii}-4x+4=30+4
Foursquare -two.
x^{ii}-4x+4=34
Add together 30 to 4.
\left(ten-2\correct)^{2}=34
Cistron x^{2}-4x+4. In general, when x^{2}+bx+c is a perfect foursquare, it can always exist factored equally \left(x+\frac{b}{2}\correct)^{2}.
\sqrt{\left(ten-2\right)^{ii}}=\sqrt{34}
Take the square root of both sides of the equation.
x-two=\sqrt{34} x-2=-\sqrt{34}
Simplify.
x=\sqrt{34}+2 x=2-\sqrt{34}
Add 2 to both sides of the equation.
ten ^ ii -4x -30 = 0
Quadratic equations such every bit this one tin be solved by a new direct factoring method that does not require guess work. To use the straight factoring method, the equation must be in the grade x^2+Bx+C=0.
r + s = 4 rs = -30
Let r and south be the factors for the quadratic equation such that x^two+Bx+C=(x−r)(ten−south) where sum of factors (r+due south)=−B and the product of factors rs = C
r = 2 - u s = 2 + u
Two numbers r and s sum up to four exactly when the boilerplate of the ii numbers is \frac{1}{ii}*4 = 2. You lot tin too run into that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2+Bx+C. The values of r and s are equidistant from the eye past an unknown quantity u. Express r and s with respect to variable u. <div way='padding: 8px'><img src='https://opalmath.azureedge.cyberspace/customsolver/quadraticgraph.png' way='width: 100%;max-width: 700px' /></div>
(2 - u) (2 + u) = -30
To solve for unknown quantity u, substitute these in the product equation rs = -30
4 - u^two = -30
Simplify past expanding (a -b) (a + b) = a^2 – b^ii
-u^2 = -30-4 = -34
Simplify the expression by subtracting 4 on both sides
u^two = 34 u = \pm\sqrt{34} = \pm \sqrt{34}
Simplify the expression by multiplying -1 on both sides and have the square root to obtain the value of unknown variable u
r =two - \sqrt{34} = -3.831 s = 2 + \sqrt{34} = seven.831
The factors r and s are the solutions to the quadratic equation. Substitute the value of u to compute the r and s.
4 X 2 X 30,
Source: https://mathsolver.microsoft.com/en/solve-problem/x%20%5E%20%7B%202%20%7D%20-%204%20x%20-%2030%20%3D%200
Posted by: landisdrecandlere.blogspot.com
0 Response to "4 X 2 X 30"
Post a Comment