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.
• x = 1.7
• x = 3.7
• x =0.77
• x =0.27
To determine which of the options is a solution to the quadratic equation -x^2 +x= -10, we can substitute each of the options into the equation and see which result is closest to zero.
If we substitute x = 1.7 into the equation, we have:
-(1.7)^2 + 1.7 = -10
-2.89 + 1.7 = -10
-1.19 ≠ -10
If we substitute x = 3.7 into the equation, we have:
-(3.7)^2 + 3.7 = -10
-13.69 + 3.7 = -10
-9.99 ≠ -10
If we substitute x = 0.77 into the equation, we have:
-(0.77)^2 + 0.77 = -10
-0.5929 + 0.77 = -10
0.1771 ≠ -10
If we substitute x = 0.27 into the equation, we have:
-(0.27)^2 + 0.27 = -10
-0.0729 + 0.27 = -10
0.1971 ≠ -10
None of the options, x = 1.7, x = 3.7, x = 0.77, or x = 0.27, are solutions to the quadratic equation -x^2 + x = -10.