Problema Solution
solve quadratic equation showin all work under the following instructions
a. move the constant term to the right side of the equation.
b. Multiply eachterm in the equation by four times the coefficient of the x2 term.
c. Squae the coefficient of the orginal x term and add it to both sides f the equation.
d. take the square root of both sides
e. set the left side of the equation equal to the positive square root of the number on the right side and solve fr x.
f. set the left side of the equation equal to the negative square root of the number on the right side of the equation and solve for x.
x2 - 2x - 13 = 0
Answer provided by our tutors
So you simply have to follow the instuctions as applied to x^2 -2x - 13=0
a. The constant term is "13", or generally, what doesn't have an "x" attached to it- just a plain number. So in this step, you move it to the right: x^2-2x=13. Remember to change the sign, what happened here was actually adding "13" to both sides of the equation.
b. The coefficient of the x^2 term is "1" (when nothing is written, it's understood to be "1"), so 4x1=4, and multiplying the equation by 4, we get: 4x^2-8x= 52.
c.The coefficient of the original x term is -2, squaring that, we get 4. Adding it to both sides, we get:
4x^2-8x+4 = 52+4=56
d. Note that 56= 14*4, so it's square root would be both positive and negative 2sqrt(14)
For the left side, we can factor out 4, so we get 4(x^2 - 2x+1), and then when you take the square root, that's 2 (square root of four) * (x-1) [recall that (x-1)^2=x^2-2x+1], so
2*(x-1)= 2x-2
e. 2x-2 = 2sqrt(14) [the positive of the right side]
Then we divide both sides by 2: x-1 = sqrt(14), and then isolating x, x= 1+ sqrt(14)
f.Likewise with the negative square root,
2x-2 = -2sqrt(14), again dividing both sides by 2: x-1=-sqrt(14), and again isolating x, x=1-sqrt(14)