4x^2-6x=-14x2−6x=−1
Factor out a 44
4(x^2-6/4x)=-14(x2−64x)=−1
Simplify fraction
4(x^2-3/2x)=-14(x2−32x)=−1
Take half of x term and square the result
((-3/2)/2)^2=((-3/2)*(1/2))^2=(-3/4)^2=9/16(−322)2=((−32)⋅(12))2=(−34)2=916
Add 4*9/164⋅916 or 9/494 to the right side because we factored out a 44.
Add 9/16916 to the left side.
4(x^2-3/2x+9/16)=-1+9/44(x2−32x+916)=−1+94
4(x-3/4)^2=-1+9/44(x−34)2=−1+94
4(x-3/4)^2=-4/4+9/44(x−34)2=−44+94, common denominators -1=-4/4−1=−44
4(x-3/4)^2=5/44(x−34)2=54
(x-3/4)^2=(5/4)/4(x−34)2=544
(x-3/4)^2=5/16(x−34)2=516
sqrt((x-3/4)^2)=+-sqrt(5/16)√(x−34)2=±√516
x-3/4=+-sqrt(5/16)x−34=±√516
x-3/4=+-sqrt(5)/4x−34=±√54
x=+-sqrt(5)/4+3/4x=±√54+34
x=(+-sqrt(5)+3)/4x=±√5+34
