31. Solve the equation by completing the square. Round to the nearest hundreth if necessary.
x^2 - 6x = 7
x = 7, 1
x = -7, 1
x = -7, -1
x = 7, -1
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
okay thanks, I was thinking that.
You are welcome :)
No thinking, just doing and CHECKING
okay...haha I'll do it...then check!! thanks Damon!
Why did the square go to the party?
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.
To solve the equation x^2 - 6x = 7 by completing the square, follow these steps:
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.