Solve the equation by completing the square. Round to the nearest hundredth if necessary.
x2 – 6x = 7
A. x = 7, 1
B. x = –7, 1
C. x = –7, –1
D. x = 7, –1
To complete the square, we need to take half of the coefficient of x (-6/2 = -3) and square it ( (-3)^2 = 9). We then add and subtract this value from both sides:
x^2 - 6x = 7
x^2 - 6x + 9 - 9 = 7
(x - 3)^2 - 9 = 7
(x - 3)^2 = 16
Taking the square root of both sides, we get:
x - 3 = ±4
x = 3 ± 4
This gives us two solutions: x = 7 and x = -1.
Rounding to the nearest hundredth is not necessary in this case since the solutions are integers, but if it were, the answer would still be the same.
Therefore, the answer is:
D. x = 7, -1.
To solve the equation x^2 - 6x = 7 by completing the square, follow these steps:
1. Move the constant term (7) to the right side of the equation:
x^2 - 6x - 7 = 0
2. Take half of the coefficient of the x-term (-6) and square it, then add it to both sides of the equation:
x^2 - 6x + (-6/2)^2 = 7 + (-6/2)^2
x^2 - 6x + 9 = 7 + 9
x^2 - 6x + 9 = 16
3. Rewrite the left side of the equation as a perfect square trinomial:
(x - 3)^2 = 16
4. Take the square root of both sides of the equation:
√[(x - 3)^2] = ±√16
x - 3 = ±4
5. Solve for x by adding 3 to both sides:
x = 3 ±4
6. Simplify the solutions:
x = 7 or x = -1
Rounding to the nearest hundredth, the solutions are:
A. x = 7, 1