x^2 - 6x - 20 = 20 can be rewritten as:
x^2 - 6x - 40 = 0.
To complete the square, take half of the coefficient of x and square it. Half of -6 is -3, and (-3)^2 = 9.
Add 9 to both sides of the equation to maintain balance:
x^2 - 6x + 9 = 40 + 9
x^2 - 6x + 9 = 49.
The left side of the equation can be factored as a perfect square:
(x - 3)^2 = 49.
Take the square root of both sides to solve for x:
x - 3 = ±√49
x - 3 = ±7.
Now, solve for x by adding 3 to both sides of the equation:
x = 3 + 7 or x = 3 - 7.
The two solutions to the equation x^2 - 6x - 20 = 20 are x = 10 or x = -4.
Complete the square to solve the following quadratic equation: x^2 - 6x - 20 = 20.
1 answer
1 answer