Quadratic equation help?

x^2-2x-1=0
x=[2 + & - (4+4)^1/2]/2=1+2^1/2 & 1-2^1/2=
=2.41 & -0.41

Q1:
x² = 2x + 1
x² - x = 1 + 1²
x² - x = 1 + 1
(x - 1)² = 2
x - 1 = 1.4142136

x = 1.4142136 + 1, x = 2.4142136
x = - 1.4142136 + 1, x = - 0.4142136

Answer: x = 2.4142136, - 0.4142136

Q2:
x² + 3 = - 8x
x² + 4x = - 3 + 4²
x² + 4x = - 3 + 16
(x + 4)² = 13
x + 4 = 3.6055513

x = 3.6055513 - 4, x = - 0.3944487
x = - 3.6055513 - 4, x = - 7.6055513

Answer: x = - 0.3944487, - 7.6055513

1) x = 1+/-sqrt2

2) x= -4+/-sqrt13

1)
x^2 = 2x + 1
x^2 - 2x - 1 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 1
b = -2
c = -1

x = [2 ±√(4 + 4)]/2
x = [2 ±√8]/2
x = [2 ±√(2^2 * 2)]/2
x = [2 ±2√2]/2
x = 1 ±√2

∴ x = 1 ±√2

= = = = = = = =

2)
x^2 + 3 = -8x
x^2 + 8x + 3 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 1
b = 8
c = 3

x = [-8 ±√(64 - 12)]/2
x = [-8 ±√52]/2
x = [-8 ±√(2^2 * 13)]/2
x = [-8 ±2√13]/2
x = -4 ±√13

∴ x = -4 ±√13

X^2 = 2x + 1
=> x^2 – 2x - 1
=> -b±√(b^2 – 4ac)/ 2a
=> 2±√(4 + 4)/2
=> 2±√(8)/2
=> 2±2√(2)/2
=> 1±√(2)

X^2 + 3 = -8x
=> x^2 + 8x + 3
=> -b±√(b^2 – 4ac)/ 2a
=> 8±√(64 -12)/2
=> 8±√(52)/2
=> 2±2√(13)/2
=> 1±√(13)

x^2 = 2x +1
x^2 - 2x - 1 = 0
now use quadratic eqtn
x = -b +-/(b^2 - 4ac)
x = 2 +-/(4 + 4)
x= 2 + /8 , 2-/8


and


x^2 + 3 = -8x
x^2 +8x + 3 = 0
quad eqtn
x = -8 +- /(16-12)
x = -8 +-/4
x = -6 , -10

x^2=2x+1

-x^2(xSquared)+2x+1=0
-2(+ or -)√2^2-4(-1)(1) all divided by 2 simplify
-2(+ or -)√4+4 all divided by 2
-2(+ - )2√2 all divided by 2
-1(+ -) √2

Answers are -1+√2 and -(1+√2)

x^2+3= -8x

x^2+8x+3=0
-8(+ or -)√8^2-4(1)(3) all divided by 2 simplify
-8(+ - )√16-12 all divided by 2
-8 (+ - )√4 all divided by 2
-8 (+ -) 2 all divided by 2
-4(+ -) 1

Answers are -3 and -5

x^2 = 2x+1 => x^2 - 2x - 1 = 0 => x = {2 ±√(4+8)}/2 = 1±√3.