Solving Quadratic Equations - Assignment Example

Download file to see previous pages The coefficient of the x term of the original equation is then squared and added to both sides of the equation.
-2 being the coefficient of the original x term. Square = -2*-2= 4
Adding 4 to both sides
〖4x〗^2-8x+4=52+4
〖4x〗^2-8x+4=56
4. Taking square roots on both sides.
√(〖4x〗^2-8x+4)=√56
√(〖(2x-2)〗^2 )=√(4*14)
2x-2=2√14
Eliminating 2 from both sides
2*(x-1)=2*√14
Dividing both sides by two
(x-1)=±√14
5. Assuming the positive value after taking the square root
(x-1)=3.742
Adding one on both sides
(x-1+1)=3.742+1
x=4.742
6. The left-hand side of the equation is set to equalize the negative square root of the number present on the right-hand side of the equation
.
(x-1)+ 1=-√14+1
x=1-√14
x=1-3.742
x=-2.742
The Final solution is: x ϵ {-2.742, 4.742}


In order to solve equation c the same six steps are followed.
(c.) x^2+12x-64=0
1. First of all the constant term is moved to the right-hand side of the equation
x^2+12x-64+64=0+64
x^2+12x-0=0+64
x^2+12x=64
2. Each term on either side of the equation is multiplied by four times of the x square’s coefficient.
〖(x〗^2+12x)*(4*1)=64*(4)
〖(x〗^2+12x)*(4)=256
〖(x〗^2)*(4)+12x*(4)=256
〖4x〗^2+48x=256
3. The coefficient of the x term of the original equation is then squared and added to both sides of the equation.
12 is the coefficient of the original x term. Square = 12*12= 144
Adding to both sides
〖4x〗^2+48x+144=256+144
〖4x〗^2+48x+144=400
4. Taking square roots on both sides.
√(〖4x〗^2+48x+144)=√400
√(〖(2x+12)〗^2 )=√(20*20)
2x+12=±20
Eliminating 2 from both sides
2*(x+6)=2*10
Dividing both sides by two
(x+6)=±10
5. Assuming the positive value after taking the square root
(x+6)=10
Subtracting six on both sides
(x+6-6)=10-6
x=4
6. The left-hand side of the equation is set to equalize the negative square root of the number present on the right-hand side of the equation. ...Download file to see next pages Read More