Question

which of the following is a solution to the quadratic equation -x^2+x=-10? assume that the solution has been rounded to the nearest hundred

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the quadratic equation -x^2+x=-10, we can rewrite it as -x^2+x+10=0.

Next, we can either apply the quadratic formula or factor the equation.

Applying the quadratic formula:
The quadratic formula is x = (-b ± √(b^2-4ac))/(2a).

In this case, a=-1, b=1, and c=10.

Plugging in these values, we get:
x = (-1 ± √(1^2-4(-1)(10)))/(2(-1))
= (-1 ± √(1+40))/(-2)
= (-1 ± √41)/(-2)

Rounding this to the nearest hundredth, we have the two solutions:
x ≈ 4.29 and x ≈ -0.29

Therefore, the correct solution rounded to the nearest hundred is x ≈ -0.29.

Answer 2

out of x=.27, x=3.7, x=1.7, x=.77

Answer 3

[AI-generated answer — Bot GPT 3.5]

None of the given options (x = 0.27, x = 3.7, x = 1.7, x = 0.77) are solutions to the quadratic equation -x^2 + x = -10.

Answer 4

[AI-generated answer — Explain Bot]

To find the solution to the quadratic equation -x^2 + x = -10, we can first rewrite the equation in standard form, which is ax^2 + bx + c = 0.

In this case, our equation becomes -x^2 + x + 10 = 0.

To solve this quadratic equation, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions can be found using the formula x = (-b ± sqrt(b^2 - 4ac)) / (2a).

In our equation, we have a = -1, b = 1, and c = 10. Plugging these values into the quadratic formula, we get:

x = (-1 ± sqrt(1^2 - 4(-1)(10))) / (2(-1))

Simplifying further:

x = (-1 ± sqrt(1 + 40)) / -2
= (-1 ± sqrt(41)) / -2

Now, to round the solution to the nearest hundred, we need to consider the decimal part. Since the square root of 41 is about 6.4, the two possible solutions become:

x = (-1 + 6.4) / -2 = 5.4 / -2 = -2.7 (rounded to the nearest hundred: -300)
x = (-1 - 6.4) / -2 = -7.4 / -2 = 3.7 (rounded to the nearest hundred: 400)

Therefore, the solutions to the quadratic equation -x^2 + x = -10, rounded to the nearest hundred, are -300 and 400.