Solve the Quadratic Equation

 Solve for x

1) x^2 = 0.64

Solution

We have to solve for 'x'

but here we are having x^2, so to make this x^2 as x,

we have to take square root on both the sides

sqrt(x^2) = sqrt(0.64)

x = +/- 0.8

2) x^2 - 50 = 50

Solution

We have to solve for x

so first let's move -50 to another side

to move -50, we have to add 50 on both sides

x^2 -50 +50 = 50 +50

x^2 +0 = 100

x^2 = 100

Now to make x^2 as x, Take square root on both sides

sqrt(x^2) = sqrt(100) 

x = +/- 10

3) 2 - x^2 = 1.51

Solution

We have to solve for x

so first let's move 2 to another side

to move 2, we have to subtract 2 on both sides

2 - x^2-2 = 1.51-2

-x^2 = -0.49 

to make -x^2 as x^2, we have to multiply by -1 on both sides
(- * - = + )

x^2 = 0.49

Take sqrt on both sides

sqrt(x^2) = sqrt(0.49)

x = +/- 0.7

4) 3x - x^2 = -144 + 3x

Solution

 3x present on both sides

if we subtract 3x on both sides then 3x gets vanished (3x-3x=0)

so, -x^2 = -144

multiply by -1 on both the sides

x^2 = 144

take sqrt on both sides

sqrt(x^2) = sqrt(144)

x = +/-12

5) -x^2 -4 = 0

Solution

To move -4 to another side, add 4 on both the sides

-x^2 -4 +4 = 0+4

-x^2 + 0 = 4

-x^2 = 4

To make -x^2 as x^2, multiply by -1 on both sides

-x^2 * -1 = 4* -1

x^2 = -4

Take sqrt on both sides

sqrt(x^2) = sqrt(-4) 

x = +/- 2i 

Note :
sqrt(-1) = i ( imaginary value )
so, sqrt(-4) = sqrt(-1*4)
                   = sqrt(-1) * sqrt(4)
                   = +/- i * 2 or +/-2i

6) 3y^2 = 48

Solution

To make 3y^2 as y^2, we have to divide by 3 on both the sides

3y^2 / 3 = 48 / 3

y^2 = 16

Take sqrt on both the sides

sqrt(y^2) = sqrt(16)

y = +/- 4

7) 6x^2 - x = 216 - x

Solution

-x is present on both the sides, so if we add x on the sides, x gets vanished 

6x^2 - x = 216 - x

6x^2 = 216 

take make 6x^2 as x^2, divide both the sides by 6

6x^2 / 6 = 216 / 6

x^2 = 36

Take sqrt on both the sides

sqrt(x^2) = sqrt(36)

x = +/- 6

8) 10+4y^2 = 115 -y^2

Solution

First, let us move 10 to the right side, so subtract 10 on both sides

10+4y^2 - 10  = 115 -y^2 -10

4y^2 = 105 -y^2

now to move -y^2 to the left side, add y^2 on both sides

4y^2 + y^2 = 105 -y^2 + y^2

5y^2 = 105

to make 5y^2 as y^2, divide both the sides by 5

5y^2 / 5 = 105 / 5

y^2 = 21

y= +/-sqrt(21)