Let x2+13x=−3 .
What values make an equivalent number sentence after completing the square?
Enter your answers in the boxes.
We can complete the square by adding and subtracting (13/2)^2 = 169/4 to both sides of the equation. This gives:
x^2 + 13x + 169/4 = 160/4
Simplifying the left side and the right side, we get:
(x + 13/2)^2 = 40
Taking the square root of both sides, we obtain:
x + 13/2 = ±sqrt(40)
Simplifying and solving for x, we get:
x = -13/2 ± 2sqrt(10)
Therefore, the values that make an equivalent number sentence after completing the square are:
x = -13/2 + 2sqrt(10) and x = -13/2 - 2sqrt(10)
they did not ask you to solve the equation.
An equivalent sentence is just
(x + 13/2)^2 = 40