Question

X^2-4x-11=0 completing the square

Answer 1

Since −11-11 does not contain the variable to solve for, move it to the right side of the equation by adding 1111 to both sides.x2+4x=11x2+4x=11To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of bb, the coefficient of xx.(b2)2=(2)2b22=22Add the term to each side of the equation.x2+4x+(2)2=11+(2)2x2+4x+22=11+22Simplify the equation.Tap for fewer steps...Simplify the right side.Tap for fewer steps...Simplify each term.Tap for more steps...x2+4x+(2)2=11+4x2+4x+22=11+4Add 1111 and 44 to get 1515.x2+4x+(2)2=15x2+4x+22=15Simplify each term.Tap for fewer steps...Remove parentheses around 22.x2+4x+22=15x2+4x+22=15Raise 22 to the power of 22 to get 44.x2+4x+4=15x2+4x+4=15Factor the perfect trinomial square into (x+2)2x+22.(x+2)2=15x+22=15Solve the equation for xx.Tap for fewer steps...Take the square root of each side of the equation to setup the solution for xx(x+2)2⋅12=±√15x+22⋅12=±15Remove the perfect root factor x+2x+2 under the radical to solve for xx.(x+2)=±√15x+2=±15Remove parentheses.x+2=±√15x+2=±15Since 22 does not contain the variable to solve for, move it to the right side of the equation by subtracting 22 from both sides.x=−2±√15

Answer 2

The answers are either:

x=2+√15 or x=2−√15

Hope this helps!