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 hundredth, if applicable.
The quadratic equation −x^2+x=−10 can be rewritten as −x^2+x+10=0. To find the solution(s) to this equation, we can use the quadratic formula: x = [-b ± sqrt(b^2-4ac)] / 2a.
In this case, 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)
x = [-1 ± sqrt(1+40)] / -2
x = [-1 ± sqrt(41)] / -2
Rounding to the nearest hundredth, the solutions are:
x ≈ -4.56 and x ≈ 3.56
Therefore, the solutions to the quadratic equation −x^2+x=−10 are approximately -4.56 and 3.56.
To find the solution(s) to the quadratic equation −x^2 + x = −10, we need to solve for x.
Step 1: Rewrite the quadratic equation in standard form:
-x^2 + x + 10 = 0
Step 2: To find the solutions, we can use either factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation -x^2 + x + 10 = 0, we can identify:
a = -1, b = 1, c = 10
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)
Step 3: Evaluate the expression:
x ≈ (-1 + √41) / (-2) ≈ 2.90
x ≈ (-1 - √41) / (-2) ≈ -1.40
Therefore, the solutions to the quadratic equation -x^2 + x = -10, rounded to the nearest hundredth, are approximately x ≈ 2.90 and x ≈ -1.40.
To solve the quadratic equation −x^2+x=−10, we can rearrange the equation to the form ax^2+bx+c=0. In this case, a = -1, b = 1, and c = 10.
To find the solution, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Plugging in the values, we get:
x = (-(1) ± √((1)^2 - 4(-1)(10))) / 2(-1)
Simplifying further:
x = (-1 ± √(1 + 40)) / (-2)
x = (-1 ± √41) / (-2)
Rounding to the nearest hundredth:
x ≈ (-1 + √41) / (-2) ≈ -3.12
or
x ≈ (-1 - √41) / (-2) ≈ 2.12
Therefore, the solutions to the quadratic equation are approximately -3.12 and 2.12.