x^2 - 6 x + (6/2)^2 = 7 + (6/2)^2
x^2 - 6 x + 9 = 7 + 9
(x-3)^2 = 16
(x-3) = 4 or (x-3) = -4
x = 7 or x = -1
check
1 + 6 = 7
49 - 42 = 7
x^2 - 6x = 7
x = 7, 1
x = -7, 1
x = -7, -1
x = 7, -1
x^2 - 6 x + 9 = 7 + 9
(x-3)^2 = 16
(x-3) = 4 or (x-3) = -4
x = 7 or x = -1
check
1 + 6 = 7
49 - 42 = 7
No thinking, just doing and CHECKING
Because it wanted to find its perfect match!
To solve the equation by completing the square, let's follow these steps:
1. First, move the constant term to the right side:
x^2 - 6x = 7 => x^2 - 6x - 7 = 0
2. To complete the square, take half the coefficient of x (-6 in this case) and square it. So, (-6/2)^2 = 9.
3. Add this value to both sides of the equation:
x^2 - 6x + 9 - 7 = 0 + 9 => x^2 - 6x + 2 = 0
4. Now, we can write the left side of the equation as a perfect square trinomial:
(x - 3)^2 - 7 = 0
5. Adding 7 to both sides:
(x - 3)^2 = 7
6. Taking the square root of both sides:
x - 3 = ±√7
7. Finally, solving for x:
x = 3 ± √7
Rounding to the nearest hundredth, we get:
x ≈ 3 + √7 ≈ 5.65
x ≈ 3 - √7 ≈ 0.35
So, the correct answer is x ≈ 5.65, 0.35.
Step 1: Write the equation in the form x^2 + bx = c
x^2 - 6x = 7
Step 2: Take half of the coefficient of x, square it, and add it to both sides of the equation.
Half of -6 is -3, and (-3)^2 = 9
x^2 - 6x + 9 = 7 + 9
x^2 - 6x + 9 = 16
Step 3: Rewrite the left side of the equation as the square of a binomial.
(x - 3)^2 = 16
Step 4: Take the square root of both sides of the equation.
x - 3 = ±√(16)
x - 3 = ±4
Step 5: Solve for x.
Case 1: x - 3 = 4
x = 4 + 3
x = 7
Case 2: x - 3 = -4
x = -4 + 3
x = -1
So the solutions to the equation x^2 - 6x = 7, rounded to the nearest hundredth, are x = 7 and x = -1.