MATH SOLVE

4 months ago

Q:
# x^2-4x-3=0solve by using completing the square

Accepted Solution

A:

Answer:3,1Step-by-step explanation:Subtract 33 from both sides of the equation.x2−4x=−3x2-4x=-3To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of bb.(b2)2=(−2)2(b2)2=(-2)2Add the term to each side of the equation.x2−4x+(−2)2=−3+(−2)2x2-4x+(-2)2=-3+(-2)2Simplify the equation.Tap for fewer steps...Raise −2-2 to the power of 22.x2−4x+4=−3+(−2)2x2-4x+4=-3+(-2)2Simplify −3+(−2)2-3+(-2)2.Tap for fewer steps...Raise −2-2 to the power of 22.x2−4x+4=−3+4x2-4x+4=-3+4Add −3-3 and 44.x2−4x+4=1x2-4x+4=1Factor the perfect trinomial square into (x−2)2(x-2)2.(x−2)2=1(x-2)2=1Solve the equation for xx.Tap for fewer steps...Take the squaresquare root of each side of the equationequation to set up the solution for xx(x−2)2⋅12=±√1(x-2)2⋅12=±1Remove the perfect root factor x−2x-2 under the radical to solve for xx.x−2=±√1x-2=±1Any root of 11 is 11.x−2=±1x-2=±1The complete solution is the result of both the positive and negative portions of the solution.Tap for fewer steps...First, use the positive value of the ±± to find the first solution.x−2=1x-2=1Move all terms not containing xx to the right side of the equation.Tap for fewer steps...Add 22 to both sides of the equation.x=1+2x=1+2Add 11 and 22.x=3x=3Next, use the negative value of the ±± to find the second solution.x−2=−1x-2=-1Move all terms not containing xx to the right side of the equation.Tap for fewer steps...Add 22 to both sides of the equation.x=−1+2x=-1+2Add −1-1 and 22.x=1x=1The complete solution is the result of both the positive and negative portions of the solution.x=3,1x=3,1