What 2 numbers when multiplied you get 21.25, but when added you get -11
Let's call the two numbers x and y. We are given that when multiplied, they equal 21.25, so we can write the equation:
xy = 21.25
We are also given that when added, they equal -11, so we can write the equation:
x + y = -11
To solve these two equations, we can use substitution. Solving the second equation for y, we get:
y = -11 - x
Substituting this expression for y in the first equation, we have:
x(-11 - x) = 21.25
Expanding and simplifying this equation, we get:
-11x - x^2 = 21.25
Rearranging this equation, we have:
x^2 + 11x + 21.25 = 0
We can now solve this quadratic equation for x. However, upon solving, we find that the quadratic equation does not have real roots. Therefore, there are no two real numbers that satisfy the given conditions (multiplication equals 21.25 and addition equals -11).
To find the two numbers that satisfy the given conditions, we can set up a system of equations. Let's represent the two numbers as x and y.
From the problem statement, we have the following information:
1. xy = 21.25 (equation 1)
2. x + y = -11 (equation 2)
To solve the system of equations, we can use substitution or elimination method. Let's use the substitution method.
Solve equation 2 for x:
x = -11 - y
Substitute this expression for x in equation 1:
(-11 - y) * y = 21.25
Expand and rearrange the equation:
-11y - y^2 = 21.25
Rearrange the equation in standard form:
y^2 + 11y + 21.25 = 0
Solve this quadratic equation using factoring, completing the square, or the quadratic formula to find the possible values of y.
Using the quadratic formula: y = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = 11, and c = 21.25.
y = (-11 ± √(11^2 - 4 * 1 * 21.25)) / (2 * 1)
y = (-11 ± √(121 - 85)) / 2
y = (-11 ± √36) / 2
y = (-11 ± 6) / 2
Now we have two possible values for y:
1. y = (-11 + 6) / 2 = -5/2 = -2.5
2. y = (-11 - 6) / 2 = -17/2 = -8.5
Substitute each value of y back into equation 2 to find the corresponding values of x:
1. When y = -2.5, x = -11 - (-2.5) = -11 + 2.5 = -8.5
2. When y = -8.5, x = -11 - (-8.5) = -11 + 8.5 = -2.5
Therefore, the two numbers are -8.5 and -2.5. When multiplied together, they equal 21.25, and when added together, they equal -11.
To find the two numbers that satisfy these conditions, we can create two equations based on the given information. Let's assume the two numbers are represented by variables, such as x and y.
From the problem statement, we have two conditions:
1. The product of the two numbers is 21.25: x * y = 21.25
2. The sum of the two numbers is -11: x + y = -11
To solve this system of equations, we can use a method called substitution or elimination. In this case, substitution is simpler. Let's solve for one variable in terms of the other in the second equation and then substitute it into the first equation.
From the second equation, we can solve for x in terms of y:
x = -11 - y
Now substitute this value of x into the first equation:
(-11 - y) * y = 21.25
Expanding the equation gives us:
-11y - y^2 = 21.25
Rearranging the equation to standard form:
y^2 + 11y + 21.25 = 0
Now we have a quadratic equation, which we can solve using factoring, completing the square, or the quadratic formula.
After factoring or using the quadratic formula, we find that the two possible solutions for y are approximately -10.25 and -0.75.
Substituting these values back into the second equation, we can determine the corresponding values of x:
When y = -10.25, x = -11 - (-10.25) = -11 + 10.25 = -0.75
When y = -0.75, x = -11 - (-0.75) = -11 + 0.75 = -10.25
Therefore, the two numbers are approximately -0.75 and -10.25. When multiplied, they give 21.25, and when added, they give -11.