How do you solve using the completing the square method #4t^2 = 8t - 1#?

Question

Julia Adams · Accepted Answer

#t=1+-(sqrt(3))/(2)#

Transfer all values that start with #t# to the left.

#4t^2-8t=-1#

To get the coefficient of #t^2# to be 1, divide everything by the initial coefficient #4#.

#b=-2#; note that #t^2-2t=-1/4#.

To both sides, add the square of half the coefficient #b#.

#1/4+(-2/2)^2=t^2-2t+(-2/2)^2#

Rewrite the right side in perfect square form and make it simpler.

#(t-1)^2=3/4#

Calculate the square root of both sides by #+-#.

#t-1=+-sqrt(3)/2#

Put one on each side.

#t=1 + -sqrt(3)/2#

Julia Adams · Answer

See details below to obtain
#color(white)("XXX")t=1+-sqrt(3)/2# #color(white)("XXX")4t^2=8t-1# is given. Obtain every term that uses the variable on the left side: #color(white)("XXX")4t^2-8t=-1# Separate both sides by #4#, so that t^2-2t= -1/4# #color(white)("XXX") In an expanded squared binomial, if the first two terms are #t^2-2t#, then the third term needs to be #1#. Add #1# to both sides to complete the square: #color(white)("XXX")t^2-2t+1 = 3/4# Make the following correction to the left side: #color(white)("XXX")(t-1)^2=3/4# Utilizing square roots, we obtain: #color(white)("XXX")t-1=+-sqrt(3)/2# Add #1# to both sides: t=1+sqrt(3)/2# and t=1-sqrt(3)/2#. #color(white)("XXX")

Savannah Anderson · Answer

undefined To solve the equation 4t^2 = 8t - 1 using the completing the square method, follow these steps:

1. Move all terms to one side of the equation to set it equal to zero: 4t^2 - 8t + 1 = 0.
2. Divide the equation by the coefficient of t^2 to make the leading coefficient equal to 1: t^2 - 2t + 1/4 = 0.
3. Rewrite the equation as a perfect square trinomial: (t - 1)^2 = 0.
4. Take the square root of both sides to isolate t - 1: t - 1 = 0.
5. Solve for t: t = 1.