Answer: StartFraction negative 1 plus-or-minus StartRoot 21 EndRoot Over 2
Step-by-step explanation:
The given quadratic equation is expressed as
x² = 5 - x
Rearranging the equation to take the standard form of ax² + bx + c, it becomes
x² + x - 5 = 0
The general formula for solving quadratic equations is expressed as
x = [- b ± √(b² - 4ac)]/2a
From the equation given,
a = 1
b = 1
c = - 5
Therefore,
x = [- 1 ± √(1² - 4 × 1 × - 5)]/2 × 1
x = [- 1 ± √(1 - - 20)]/2
x = [- 1 ± √21]/2
x = (- 1 + √21)/2 or x = (- 1 - √21)/2
Answer:
16a^2+2
Step-by-step explanation:
<span>sqrt(3x+7)=x-1 </span>One solution was found : <span> x = 6
</span>Radical Equation entered :
<span> √3x+7 = x-1
</span>
Step by step solution :<span>Step 1 :</span>Isolate the square root on the left hand side :
Radical already isolated
<span> √3x+7 = x-1
</span>
<span>Step 2 :</span>Eliminate the radical on the left hand side :
Raise both sides to the second power
<span> (√3x+7)2 = (x-1)2
</span> After squaring
<span> 3x+7 = x2-2x+1
</span>
<span>Step 3 :</span>Solve the quadratic equation :
Rearranged equation
<span> x2 - 5x -6 = 0
</span>
This equation has two rational roots:
<span> {x1, x2}={6, -1}
</span>
<span>Step 4 :</span>Check that the first solution is correct :
Original equation
<span> √3x+7 = x-1
</span> Plug in 6 for x
<span> √3•(6)+7 = (6)-1
</span> Simplify
<span> √25 = 5
</span> Solution checks !!
Solution is:
<span> x = 6
</span>
<span>Step 5 :</span>Check that the second solution is correct :
Original equation
<span> √3x+7 = x-1
</span> Plug in -1 for x
<span> √3•(-1)+7 = (-1)-1
</span> Simplify
<span> √4 = -2
</span> Solution does not check
2 ≠ -2
One solution was found : <span> x = 6</span>
N • 3 + 7 = 25
(n represents the unknown number)
I hope this helps
Answer:
1. The tetrahedron has 4 vertices, 6 edges and 4 faces. Then V-E+F=4-6+4=2
2. The cube has 8 vertices, 12 edges and 6 faces. Then V-E+F=8-12+6=2
3. The octahedron has 6 vertices, 12 edges and 8 faces. Then V-E+F=6-12+8=2
4. The icosahedron has 12 vertices, 30 edges and 20 faces. Then V-E+F=12-30+20=2
5. The dodecahedron has 20 vertices, 30 edges and 12 faces. Then V-E+F=20-30+12=2.