How do you solve #x^2 - 3x = -6x - 1#?

Question

Eva Adamson · Accepted Answer

The solutions for the expression are
#color(green)(x=(-3-sqrt5)/2, x=(-3+sqrt5)/2# #x^2−3x=−6x−1# #x^2−3x+6x+1=0# #x^2+3x+1=0# The equation is of the form #color(blue)(ax^2+bx+c=0# where: #a=1, b=3, c=1# The Discriminant is given by: #Delta=b^2-4*a*c# # = (3)^2-(4*(1)*1)# # = 9-4=5# As #Delta>0# there are two solutions. The solutions are found using the formula #x=(-b+-sqrtDelta)/(2*a)# #x = ((-3)+-sqrt(5))/(2*1) = (-3+-sqrt(5))/2# The solutions for the expression are: #color(green)(x=(-3-sqrt5)/2, x=(-3+sqrt5)/2#

Ethan Adkins · Answer

undefined To solve the equation $x^2 - 3x = -6x - 1$, follow these steps:

Step 1: Move all terms to one side to set the equation to zero.
$x^2 - 3x + 6x + 1 = 0$

Step 2: Combine like terms.
$x^2 + 3x + 1 = 0$

Step 3: Now, you can solve this quadratic equation using factoring, completing the square, or the quadratic formula. If factoring isn't feasible, you can use the quadratic formula which states:
$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$

In this equation, $a = 1$, $b = 3$, and $c = 1$.

Step 4: Substitute the values of $a$, $b$, and $c$ into the quadratic formula and solve for $x$.