Which of the following is a solution to the quadratic equation −x2+x=−10 ? Assume that the solution has been rounded to the nearest hundredth, if applicable.(1 point) Responses x=0.77 x equals 0.77 x=0.27 x equals 0.27 x=1.7 x equals 1.7 x=3.7 x equals 3.7
To find the solutions to the quadratic equation −x^2+x=−10, we need to set the equation equal to 0:
−x^2+x+10=0
Next, we can solve this equation using the quadratic formula:
x = (-b ± √(b^2-4ac))/(2a)
In this equation, a = -1, b = 1, and c = 10. Substituting these values into the quadratic formula, we have:
x = (-(1) ± √((1)^2-4(-1)(10)))/(2(-1))
x = (-1 ± √(1+40))/(-2)
x = (-1 ± √41)/(-2)
Rounded to the nearest hundredth, the solutions are approximately x = 0.77 and x = -2.77. Therefore, the correct solution from the given options is x = 0.77.
To find the solution to the quadratic equation −x^2 + x = −10, follow these steps:
Step 1: Rewrite the equation in standard form, setting it equal to zero:
−x^2 + x + 10 = 0
Step 2: Use the quadratic formula to find the solutions. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the given equation, a = -1, b = 1, and c = 10. Substituting the values into the formula, we get:
x = (-(1) ± √((1)^2 - 4(-1)(10))) / (2(-1))
x = (-1 ± √(1 + 40)) / (-2)
x = (-1 ± √41) / (-2)
Step 3: Simplify the solution. Rounding to the nearest hundredth, we have:
x ≈ (-1 + 6.40) / (-2) ≈ 2.40 / (-2) ≈ -1.20
x ≈ (-1 - 6.40) / (-2) ≈ -7.40 / (-2) ≈ 3.70
Therefore, the solutions to the quadratic equation −x^2 + x = −10, rounded to the nearest hundredth, are:
x ≈ -1.20 and x ≈ 3.70
Among the given options, x = 3.7 is the correct solution.
To find the solution to the quadratic equation −x^2+x=−10, you can use the quadratic formula. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the given equation, we can rewrite it in the standard form ax^2 + bx + c = 0 as -x^2 + x + 10 = 0.
By comparing this equation with the standard form, we can determine a = -1, b = 1, and c = 10.
Now, substitute these values into the quadratic formula:
x = (-1 ± √(1^2 - 4(-1)(10))) / (2(-1))
Simplifying further:
x = (-1 ± √(1 + 40)) / (-2)
x = (-1 ± √41) / (-2)
The two solutions are:
x = (-1 + √41) / (-2) ≈ 1.70 (rounded to the nearest hundredth)
x = (-1 - √41) / (-2) ≈ 3.73 (rounded to the nearest hundredth)
Therefore, the correct solution to the quadratic equation −x^2+x=−10, rounded to the nearest hundredth, are:
x ≈ 1.70 and x ≈ 3.73.
So, the option x equals 1.7 and x equals 3.7 is the correct response.