31. Solve the equation by completing the square. Round to the nearest hundredth if necessary.

x2 – 6x = –8

the real answer is

x = 4,2

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Let's solve the equation by completing the square.

First, we'll rearrange the equation to make the x terms on one side:

x^2 - 6x + 8 = 0

Now let's complete the square to find the perfect square trinomial:

(x - 3)^2 - 9 + 8 = 0

(x - 3)^2 - 1 = 0

(x - 3)^2 = 1

Taking the square root of both sides, we have:

x - 3 = ±1

x = 3 ± 1

x = 4 or x = 2

So the solutions to the equation are x = 4 and x = 2, rounded to the nearest hundredth. But since there is no decimal involved in this equation, we don't need to round. Therefore, our final solutions are x = 4 and x = 2.

To solve the equation x^2 - 6x = -8 by completing the square, follow these steps:

Step 1: Move the constant term (-8) to the other side of the equation by adding 8 to both sides:
x^2 - 6x + 8 = 0

Step 2: Divide the coefficient of the x-term (-6) by 2, and then square the result. Add this value to both sides of the equation:
x^2 - 6x + (6/2)^2 = 8 + (6/2)^2
x^2 - 6x + 9 = 8 + 9
x^2 - 6x + 9 = 17

Step 3: Rewrite the left side of the equation as a perfect square trinomial. To do this, take the square root of the coefficient of x, divide it by 2, and square the result. Replace the middle term with the perfect square trinomial:
(x - 3)^2 = 17

Step 4: Take the square root of both sides of the equation to isolate x:
√(x - 3)^2 = ±√17
x - 3 = ±√17

Step 5: Solve for x by adding 3 to both sides of the equation:
x = 3 ± √17

Therefore, the solutions to the given equation are x = 3 + √17 and x = 3 - √17.

To solve the equation x^2 - 6x = -8 by completing the square, follow these steps:

Step 1: Move the constant term (-8) to the right side of the equation:
x^2 - 6x + 8 = 0

Step 2: Divide the coefficient of x by 2, square it, and add it to both sides of the equation:
x^2 - 6x + (6/2)^2 = 8 + (6/2)^2

Simplifying this:
x^2 - 6x + 9 = 8 + 9

Step 3: Simplify both sides of the equation:
x^2 - 6x + 9 = 17

Step 4: Write the left side of the equation as a squared binomial:
(x - 3)^2 = 17

Step 5: Square root both sides of the equation:
√(x - 3)^2 = ±√17

Step 6: Solve for x:
x - 3 = ±√17

Step 7: Add 3 to both sides of the equation to get x alone:
x = 3 ±√17

Rounded to the nearest hundredth, the solutions are:
x ≈ 3 + √17 ≈ 6.12
x ≈ 3 - √17 ≈ -0.12

Hence, the solutions to the equation x^2 - 6x = -8, rounded to the nearest hundredth if necessary, are approximately x ≈ 6.12 and x ≈ -0.12.

x^2-6x=-8

x^2 -6x + ? +8=0

half of -6, squared is nine. we have 8 already so add 1 to each side.

x^2-6x+9=1
(x-3)^2=1^2

x-3= +- 1
x=2, or x=4