解:
3x²+6x-5=0
3x²+6x=5 方程两边同时除以3
x²+2x=5/3
x²+2x+1=5/3+1
(x+1)²=8/3
x+1=±√(8/3)
x+1=±2√6/3
x=(-3±2√6)/3
x1=(-3+2√6)/3
x2=(-3-2√6)/3
4x²-x-9=0
4x²-x=9 方程两边同时除以4
x²-(1/4)x=9/4
x²-(1/4)x+(1/8)²=9/4+(1/8)²
(x-1/8)²=145/64
x-1/8=±√(145/64)
x-1/8=±√145/8
x=(1±√145)/8
x1=(1+√145)/8
x2=(1-√145)/8
3x²+6x-5=0
x²+2x-5/3=0
x²+2x=5/3
x²+2x+1=5/3+1
(x+1)²=8/3
x+1=(±2√6)/3
x=(±2√6)/3-1
x1=(2√6)/3-1,x2=(-2√6)/3-1
2)4x²-x-9=0
x²-1/4x-9/4=0
x²-1/4x=9/4
x²-1/4x+1/64=9/4+1/64
(x-1/8)²=145/64
x-1/8=±√145/8
x=±√145/8+1/8
x1=√145/8+1/8,x2=-√145/8+1/8