How do you solve #x^2-2x=8#?

Question

Hazel Anglin · Accepted Answer

#color(blue)(x=-2#
# color(blue)(x=4# #x^2−2x- 8 = 0# We can Split the Middle Term of this expression to factorise it and thereby find the solutions: In this technique, if we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that: #N_1*N_2 = a*c = 1*-8 = -8# AND #N_1 +N_2 = b = -2# After trying out a few numbers we get #N_1 = -4# and #N_2 =2# #2*(-4) = -8# and #2 + (-4)= -2# #x^2−2x- 8 = x^2 color(blue)(- 4x + 2x)- 8# #= x( x-4) + 2(x - 4)# #color(blue)((x+2) ( x-4)# is the factorised form for the expression, we now equate the factors to zero and obtain the solutions. #x+2 = 0, color(blue)(x=-2# #x-4 = 0, color(blue)(x=4#

Ethan Adkins · Answer

undefined To solve the equation $x^2 - 2x = 8$, follow these steps:

1. Rearrange the equation to set it equal to zero: $x^2 - 2x - 8 = 0$.
2. Factor the quadratic equation, if possible.
3. If factoring isn't feasible, use the quadratic formula: $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$, where $a$, $b$, and $c$ are the coefficients of the quadratic equation.
4. Substitute the values of $a$, $b$, and $c$ into the quadratic formula and solve for $x$.
5. Check the solutions by substituting them back into the original equation to verify their validity.