Maths help. Solve for x. x^2 + x = 1?

Rearrange to get x^2 + x -1 =0

This can't be factorised into the form ( )( ) =0
so use the quadratic formula.

The solutions (roots) are x = -0.5 + 0.5(sqr root of 5) = 0.618

and x = -0.5 - 0.5(sqr root of 5) = -1.618

x² + x = 1
x² + 1/2x = 1 + (1/2)²
x² + 1/2x = 4/4 + 1/4
(x + 1/2)² = 5/4
x + 1/2 = +/- 1.118034

x = 1.118034 - 0.5, x = 0.618034
x = - 1.118034 - 0.5, x = - 1.618034

Answer: x = 0.618034, - 1.618034

Proof (x = 0.618034):
0.618034² + 0.618034 = 1
0.381966 + 0.618034 = 1
1 = 1

Proof (x = - 1.1618034):
(- 1.1618034)² + (- 1.1618034) = 1
2.618034 - 1.1618034 = 1
1 = 1

It does not factorize. So use the general solution.
x = (-b +/-sqrt(b^2 - 4ac))/2a
x = [-1 +/-sqrt(5)]/2 = 0.62, -1.6

question selection a million : For this equation x^2 - x - 12 = 0 , answer here questions : A. locate the roots using Quadratic formulation ! answer selection a million : The equation x^2 - x - 12 = 0 is already in a*x^2+b*x+c=0 style. via matching the consistent place, we are able to derive that the cost of a = a million, b = -a million, c = -12. 1A. locate the roots using Quadratic formulation ! keep in mind the formulation, x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a) We had understand that a = a million, b = -a million and c = -12, we in basic terms ought to subtitute the cost of a,b and c interior the abc formulation. So x1 = (-(-a million) + sqrt( (-a million)^2 - 4 * (a million)*(-12)))/(2*a million) and x2 = (-(-a million) - sqrt( (-a million)^2 - 4 * (a million)*(-12)))/(2*a million) which could be became into x1 = ( a million + sqrt( a million+40 8))/(2) and x2 = ( a million - sqrt( a million+40 8))/(2) Which make x1 = ( a million + sqrt( 40 9))/(2) and x2 = ( a million - sqrt( 40 9))/(2) We have been given x1 = ( a million + 7 )/(2) and x2 = ( a million - 7 )/(2) So we've the solutions x1 = 4 and x2 = -3

x^2+x-1=0

a=1 b=1 c=-1

-1+/- 1^2-4(1)(-1)/2

-1+/- sq rt 1+4/2
x=-1+/- sq rt 5/2

x^2 + x = 1
x^2 + x/2 + x/2 = 1
x^2 + x/2 + x/2 + 1/4 = 1 + 1/4
(x^2 + x/2) + (x/2 + 1/4) = 4/4 + 1/4
x(x + 1/2) + 1/2(x + 1/2) = 5/4
(x + 1/2)(x + 1/2) = 5/4
(x + 1/2)^2 = 5/4
x + 1/2 = ±√(5/4)
x = -1/2 ±(√5)/2
x = (-1 ±√5)/2

x= -1+/-sqrt5/2

x ² + x - 1 = 0

x = [ - 1 ± √ ( 1 + 4 ) ] / 2

x = [ - 1 ± √ 5 ] / 2

to complete the square add ¼ to both sides
x² + x + ¼ = 1 + ¼ = 5/4

now factor
(x + ½)² = 5/4

to solve for x, take square roots and subtract ½
x = - ½ ± ½ √5