Question

Exercise 6

1
Solve for x by completing the square;
a
x² - 2x - 4 = 0
bu x2 - 4x - 2 = 0
С x2 + 8x + 5 = 0
X x² + 22x - 150
e
x2 - 7x + 10 = 0
f x² + 5x-2=0
g x2 + 9x - 4 = 0
h x2 - 3x - 6 = 0​

Answer 1

`a)\\\\x^2-2x-4=0\\\\x^2-2x=4\\\\x^2-2x+1^2=4+1^2\\\\(x-1)^2=5\\\\x-1=\pm\sqrt5\\\\\underline{x=\pm\sqrt5+1\approx-1.24\ or\ 3.24}\\\\\\b)\\\\x^2-4x-2=0\\\\x^2-4x=2\\\\x^2-4x+2^2=2+2^2\\\\(x-2)^2=6\\\\x-2=\pm\sqrt6\\\\\underline{x=\pm\sqrt6+2\approx-0.45\ or\ 4.45}`

`c)\\\\x^2+8x+5=0\\\\x^2+8x=-5\\\\x^2+8x+4^2=-5+4^2\\\\(x+4)^2=11\\\\ x+4=\pm√(11)\\\\\underline{x=\pm√(11)-4\approx-7.32\ or\ -0.68}\\\\\\x)\\\\x^2+22x-15=0\\\\x^2+22x=15\\\\x^2+22x+11^2=15+11^2\\\\(x+11)^2=136\\\\x+11=\pm√(136)\\\\\underline{x=\pm√(136)-11\approx-22.66\ or\ 0.66}`

`e)\\\\x^2-7x+10=0\\\\x^2-7x=-10\\\\x^2-7x+(\frac72)^2=-10+(\frac72)^2\\\\x^2-7x+(\frac72)^2=-10+(\frac72)^2\\\\(x-\frac72)^2=-\frac{20}4+\frac{49}4\\\\ (x-\frac72)^2=\frac{29}4\\\\x-\frac72=\pm\sqrt{\frac{29}4}\\\\ \underline{x=\pm\frac{√(29)}2+\frac72\approx6.19\ or\ 0.81}\\\\\\f)\\\\x^2+5x-2=0\\\\x^2+5x=2\\\\x^2+5x+(\frac52)^2=2+(\frac52)^2\\\\(x+\frac52)^2=2+6.25 \\\\x+\frac52=\pm√(8.25)\\\\\underline{x=\pm√(8.25)-\frac52\approx-5.37\ or\ 0.37}`

`g)\\\\x^2+9x-4=0\\\\x^2+9x=4\\\\x^2+9x+(\frac92)^2=4+(\frac92)^2\\\\(x+\frac92)^2=4+20.25\\\\x+\frac92=\pm√(24.25)\\\\\underline{x=\pm√(24.25)-4.5\approx-9.42\ or\ 0.52}`

`h)\\\\x^2-3x-6=0\\\\x^2-3x=6\\\\x^2-3x+(\frac32)^2=6+(\frac32)^2\\\\(x-\frac32)&^2=6+2.25\\\\x-\frac32=\pm√(8.25)\\\\ \underline{x=\pm√(8.25)+1.5\approx4.37\ or-1.37}`